Multicriteria Relocation Analysis of an Off-site
Radioactive Monitoring Network for a Nuclear
Power Plant
NI-BIN CHANG*
Department of Civil and Environmental Engineering University of Central Florida
Orlando, Florida 32816, USA
SHU-KUANG NING
Department of Civil and Environmental Engineering National University of Kaohsiung
Nan-Tzu District 811, Kaohsiung, Taiwan
JEN-CHANG CHEN
U-Tech Technology Corporation Kaohsiung, Taiwan
ABSTRACT / Due to increasing environmental conscious-ness in most countries, every utility that owns a commercial nuclear power plant has been required to have both an on-site and off-site emergency response plan since the 1980s. A radiation monitoring network, viewed as part of the emergency response plan, can provide information regarding the radiation dosage emitted from a nuclear power plant in a regular operational period and/or abnormal measurements in an emergency event. Such monitoring information might help field operators and decision-makers
to provide accurate responses or make decisions to protect the public health and safety. This study aims to conduct an integrated simulation and optimization analysis looking for the relocation strategy of a long-term regular off-site mon-itoring network at a nuclear power plant. The planning goal is to downsize the current monitoring network but maintain its monitoring capacity as much as possible. The monitor-ing sensors considered in this study include the thermolu-minescence dosimetry (TLD) and air sampling system (AP) simultaneously. It is designed for detecting the radionuclide accumulative concentration, the frequency of violation, and the possible population affected by a long-term impact in the surrounding area regularly while it can also be used in an accidental release event. With the aid of the calibrated Industrial Source Complex–Plume Rise Model
Enhancements (ISC-PRIME) simulation model to track down the possible radionuclide diffusion, dispersion, transport, and transformation process in the atmospheric environ-ment, a multiobjective evaluation process can be applied to achieve the screening of monitoring stations for the nuclear power plant located at Hengchun Peninsula, South Taiwan. To account for multiple objectives, this study calculated preference weights to linearly combine objective functions leading to decision-making with exposure assessment in an optimization context. Final suggestions should be useful for narrowing the set of scenarios that decision-makers need to consider in this relocation process.
The nuclear power industry has provided society with economic benefits in the past decades. However, the lessons learned from the Three Mile Island (TMI) accident in the United States, the Mihama SG tube rupture in Japan, and the Chernobyl disaster in Russia have resulted in a long-term debate of the operational safety and emergency responses when using a nuclear power supply. The safety concerns of emergency
preparedness and response issues have been elevated to a considerably higher level. In most countries, each utility that owns a commercial nuclear power plant has been required to have both on-site and off-site moni-toring plans. Radiation monimoni-toring not only for the regular measurement but also in response to those accidental release events plays an important role in management decision-making. It can provide the radiation dosage emitted from a nuclear power plant in a regular operational period and/or abnormal mea-surements in an emergency event. In the week follow-ing the accident at Chernobyl in 1986, for example, elevated levels of radioactivity were detected by regular sampling and monitoring in air, rainwater, soil, and food in many European countries. The radionuclides detected in the air in these countries included iodine-KEY WORDS: Nuclear power plant; Monitoring network; Multi
objective programming; Multi criteria decision-making; Air quality model; ISC-PRIME
Published online May 4, 2006
*Author to whom correspondence should be addressed; email: [email protected]
131 (I-131), cesium-137 (Cs-137), cesium-134 (Cs-134), tellurium-132 (Te-132), ruthenium-103 (Ru-103), molybdenum-99 (Mo-99), neptunium-239 (Np-239), and northbound-95 (Nb-95) (Abagyan and others 1986). Both on-site and off-site deployment of radia-tion monitoring networks have been viewed as part of the emergency response plan to inform the public and decision-makers as to the dangers associated with the emergency.
The objective of such a deployment is to assist in public awareness of radiation impact on a regular basis or in the accidental event by improving (1) radioactive effluent monitoring, (2) dose analysis for accidental releases of radioactive particulates, radioiodine (I), tritium (3H), carbon-14 (14C), noble gases, and alpha-emitters, (3) the control of radioactivity released into the liquid pathway, (4) the measurement of off-site radiation doses, and (5) the ability to rapidly deter-mine off-site doses from radioactivity release by mete-orological and hydrological measurements so that population-protection decisions can be made appro-priately (US Nuclear Regulatory Commission, 2004).
In making environmental exposure measurements at nuclear facilities, the monitoring networks installed in the impact zone often include the high-pressure ion chamber (HPIC), the thermoluminescence dosimetry (TLD) and air sampling (AP) systems. The environ-mental dose rate measurements can be collected using the HPIC. The TLD utilizes routine dosimeters to determine the absorbed dose in a material irradiated by ionizing radiation, such as gamma-rays, X-rays, and electrons. Examples of materials useful as TLDs in-clude lithium fluoride (LiF), calcium fluoride (CaF2),
calcium sulfate (CaSO4), lithium borate (Li2B4O7),
and aluminum oxides (Al2O3). In some cases, an
electret ion chamber (EIC) can be used to replace TLD and HPIC measurements. The AP can be a fixed or portable sampling kit that is comprised of small-sized gamma-radiation detector units, which can be inde-pendently installed at the environmental monitoring sites. Some other portable sensors can sample the air or liquid in the trap to determine the exposure level. For example, the air might be sampled and passed through a bubbler system into a solution that traps the tritium particles in moisture vapor. Sensors might be installed together site by site to form a collective mea-surement capacity and ease the managerial efforts as well. Arbitrary deployment of monitoring stations might not be cost-effective due to natural variations of the meteorological system and terrain effects. For example, if the stations are located on the leeward or the terrain barrier, they could not play the role of effective monitoring; therefore, the investment is
problematic. The question left is how do we design a multicriteria evaluation procedure to screen those candidate sites and narrow down the options in a sys-tematic way so as to improve the deployment or relo-cation strategy.
Various statistical and optimization models have been applied to aid in designing a representative air quality monitoring station (AQMS). For pollutant-spe-cific cases, monitoring networks were normally de-signed and deployed with respect to SOx and NOx
in many urban regions (Smith and Egan 1979; Handscombe and Elson 1982; Graves and others 1981; Pickett and Whiting 1981; Egmond and Onderdelin-den 1981; Nakamori and Sawaragi 1984; Modak and Lohani 1985a, 1985b; Liu and others 1986; McElroy and others 1986; Baldauf and others 2001). Given the recent concerns of multipollutantsÕ impacts, more sophisticated approaches have been required. Modak and Lohani (1985c) considered siting a multipollutant AQMS with two objectives, including the design prin-ciples of minimum spanning tree (MST) and the utility function for siting the AQMSs in the Taipei metro-politan region. Langstaff and others (1987) applied an air quality simulation model and population exposure information to produce representative and combined patterns that employ the concept of sphere of influ-ence (SOI) and figure of merit (FOM) to determine the minimum number of sites. In recent studies, using the utility function in a multiobjective framework has become one of the main focuses (Trujillo-Ventura and Ellis 1991; Arbeloa and others 1993; Kainuma and others 1990). For siting the AQMS, Chang and Tseng (1999) and Tseng and Chang (2001) integrated the primary, quasistable, and reactive pollutants within a multiobjective framework. The approach was applied to assess both expansion and relocation strategies of the AQMS in a metropolitan region by gray and ge-netic algorithm-based compromise programming models. This technique, using the criterion of mini-mum distance from the ideal solution, is frequently used for solving various multiobjective decision analysis problems. Thus the noninferior solutions and trade-offs among the objectives could allow an agreement.
This study aims to conduct an integrated simulation and optimization analysis via a two-stage procedure looking for the relocation strategy of a long-term reg-ular off-site monitoring network at a nuclear power plant. The planning goal is to downsize the current monitoring network but maintain its monitoring capacity as much as possible. The monitoring sensors considered in this study include TLD and AP simulta-neously. It is designed for detecting the radionuclide accumulative concentration, the frequency of violation,
and the possible population affected by such an impact in the surrounding area regularly while it can also be used in an accidental release event. With the aid of the calibrated Industrial Source Complex–Plume Rise Model Enhancements (ISC-PRIME) simulation model to track down the possible radionuclide diffusion, dis-persion, transport, and transformation process in the atmospheric environment, a multiobjective evaluation process can be applied to achieve the screening of monitoring stations for the nuclear power plant lo-cated at Hengchun Peninsula, South Taiwan. To ac-count for multiple objectives, this study has used preference weights to linearly combine objective functions based on a goal-programming model, linking decision-making with exposure assessment. To improve the accuracy of modeling the diffusion and dispersion process, a wind tunnel test has been designed in a separate study to compare the performance between the ISC-PRIME model, which is comprised of the ISC and PRIME, and the conventional Industrial Source Complex Short-Term (ISCST3) model (Chen and Chang 2005). The ISC-PRIME model has been selected as the representative model to account for both building wakes around the plant area and the short-term dispersion over the local terrain. With the aid of the calibrated ISC-PRIME model in the first stage, a multiobjective evaluation process with a linear pro-gramming technique has been applied to achieve the screening process of monitoring stations for the nu-clear power plant in the second stage. There are four planning scenarios associated with various upper bounds of the total number of monitoring stations and preference weights of the planning objective. The monitoring system in which TLD and AP can be con-solidated into one optimized network that might be used in conjunction with the on-site monitoring net-work within the power plant in the operational period and employed as part of the emergency response sys-tem in any emergency events. The results would lead to a search for the most effective relocation strategies.
Study Area Description
Taiwan is a small island in an area of 36,000 km2 with a very high population density (636 capita/km2), where 80% of the land is mountainous area. Hence, the majority of people live in several metropolitan re-gions, such as Taipei, Kaohsiung, and Taichung. Nu-clear power supply, meeting 15.5% of the total demand for electricity in 2003, is one of the important energy sources in Taiwan. There are four nuclear power plants on this island. Three of them are currently in opera-tion, in which two of them are located at northern
Taiwan [the Kinshan plant (No.1) and Kuoshin plant (No.2)] and one is located at southern Taiwan [the Maanshan plant (No.3)]. See Table 1 for information on these plants. The on-going construction and oper-ation of the fourth nuclear power plant in northern Taiwan has brought challenges in the context of the scale of its potential risks and associated emergency preparedness and response actions in the 1990s. In Taiwan, the accidents at nuclear power plants are generally classified into four grades according to the degree of severity: Class 1 (unusual event), Class 2 (alert event), Class 3 (site-specific emergency), and Class 4 (regional emergency). Each class might have several subclasses to delineate different sublevels of severity. In recent years, minor accidental release events occurred at the first and third nuclear power plants in Taiwan, which had caused much public attention. In 2001, an emergency event happened in the Maanshan plant that was classified as a 3A Class event. It represented the most severe event in the his-tory of the nuclear power industry in Taiwan. Figure 1 indicates the population distribution near the Maan-shan plant. Because its neighboring beach area has long been a hot tourist spot in southern Taiwan, the actual population that might be affected by any acci-dental event in the Maanshan plant must be much greater than just the local residents. Therefore, the surrounding area (i.e., 17 km · 15 km) of the Maan-shan plant (No.3) was selected as the study area in this article.
Environment monitoring for the transfer media and receptors, covering air, soil, seawater, organism, and crop has been implementing by the government agency periodically. For the gaseous medium, three kinds of monitoring station were installed to detect possible radiation emission. A HPIC system was ar-ranged within the interior of the plant to detect the transient variation of direct radiation dosage (lSv/h). The TLD system was deployed in an area with a radius of 50 km around the plant. It aims to measure the accumulation of direct radiation dosage (mSv/h). The AP system was set on the leeward side of the plant to measure the radionuclide and gross beta activity of suspended solids in the air (mBq/m3). Figure 2 shows the topography and the existing monitoring stations, including the TLD and AP systems, in the area sur-rounding the Maanshan plant. The locations of these monitoring stations were decided in a subjective way in the past. Yet, budget limitation has motivated a sub-stantial reduction of the total number of these stations. Decision support systems (DSSs) have been developed over 10 years and successfully implemented in many subjects. Recent experience has demonstrated that
systems analysis applied to environmental issues at a regional, national, or even international level might significantly increase the capacity to respond to disas-ters (Hamit 1997; Li and Yang 1997; Xu and others 1996; Zhu and Stillman, 1995). It is the aim of this article to narrow the set of scenarios by a more impersonal and effective way that decision-makers need to consider in this relocation process using a comprehensive systems analysis.
Analytical Approach
A two-stage analysis, combining simulation and optimization models, was designed to achieve the aforementioned study goal. In the first step, the ISC-PRIME model was used as a simulation tool to trace the radionuclidesÕ diffusion, dispersion,
trans-port, and transformation in the study area, based on the existing meteorological databases, emission inven-tory, and terrain information. The study area was di-vided into a continuous grid system and each grid represents a candidate site for evaluation. Yet, the re-lease magnitude is related to the accidents severity of the nuclear power plant. Because any emergency case reflects an extreme condition that can hardly be used as a normal design scheme, the supportive emission inventory is thus selected based on year-round emission data collected at all roof vents and stacks in the plant. Those source terms might vary to some extent in vari-ous events depending on the heat release and the subsequent plume rise; the doses can be spatially quite different than the designed scenario. Many simulators designed for emergency response events can be used to simulate the source terms in various scenarios. The Table 1. The information of nuclear power plants in Taiwan
Plant 1 2 3
Date of start-upa #1: Dec. 1978 #1: Dec. 1981 #1: July 1984
#2: Jul. 1979 #2: Mar. 1983 #2: May. 1985
Capacity 636 kw · 2 985 kw · 2 951 kw · 2
Pattern of reactor Boiling water reactor Boiling water reactor Pressurized Water reactor
a#1: the first-generation unit; #2: the second-generation unit.
216000 218000 220000 222000 224000 226000 228000 230000 TM2-E (m) 2424000 2426000 2428000 2430000 2432000 2434000 2436000 2438000 2440000 TM2-N (m) (capita /km2) 31 to 89 89 to 143 143 to 182 182 to 326 326 to 4018
Figure 1. The population distribution in the study area.
216000 218000 220000 222000 224000 226000 228000 230000 TM2-E (m) 2424000 2426000 2428000 2430000 2432000 2434000 2436000 2438000 2440000 TM2-N (m) TLD309TLD308 TLD310 TLD311 TLD312 TLD313 TLD314 TLD319 TLD320 TLD321 TLD322 TLD323 TLD324 TLD325 TLD326 TLD327 TLD328 TLD329 TLD330 TLD331 TLD332 TLD333 TLD335 TLD336 TLD337 TLD339 TLD340 NPP3 216000 21800 0 220000 222000 224000 226000 228000 230000 TM2-E (m) 2424000 2426000 2428000 2430000 2432000 2434000 2436000 2438000 2440000 2442000 TM2-N (m) AP301 AP302 AP303 AP304 AP305 AP306 AP307 AP308 AP309 AP310 AP311 AP312 AP313 AP314 AP315 AP316 AP317 AP318 AP319 AP320 AP321 AP322 AP323 NPP3 Gulf A
TLD
BAP
Gulf Figure 2. The topographic chart and existing
monitoring stations: (A) thermoluminescence dosimetry (TLD); (B) air sampling system (AP).
wind tunnel test, described in a companion study, was used as a basis for model calibration and validation at different situations (Chen and Chang 2005).
A simulation step, however, might provide invalu-able information for indicating where the spots of highest concentration or dosage of interest are and how frequent the violation is for each type of radio-nuclide at every candidate site. With such an under-standing, the next step is to select the design objectives, constraints, and target pollutants for the multiobjective evaluation models that might provide a set of site relocation strategies. Based on such simulation results, the determination of frequency of violation, or the estimation of accumulated concentration of radionuc-lides at each candidate site on an annual basis, be-comes available when building up the objective functions and constraints required for the subsequent multiobjective evaluation analysis.
Objective functions were selected based on relevant studies and the managerial goals employed by the power plant (Tseng and Chang 2001). Subject to the budget constraint, final assessment can be found so that the compromise solution can be satisfied with re-spect to site coverage, correlation impacts, population density, and some other criteria. Even though public acceptance and public confidence could affect the decision-making, these factors are difficult to quantify before going into the choice of number of monitors. It can be taken into account later on a case-by-case basis. To reduce the managerial efforts, both TLD and AP systems are to be consolidated into the same network via the use of such a multiobjective evaluation scheme. This implies that each of the final candidate sites picked up by the model would be suitable for both types of monitoring system. The preference weights associated with objectives were drawn using an explic-itly designed questionnaire and a nonpreemptive goal-programming model to aid in decision analysis. Respondents with domain knowledge in the field sup-port this collective decision analysis, which actually combines exposure assessment with decision-making. Figure 3 demonstrates the logic flows of the two-stage analytical procedure employed in this study. They will be illustrated in great detail in the following sections.
Simulation Analysis
The continued operation of nuclear facilities simi-lar to the Chernobyl nuclear power plant in the states of the former Soviet Union has led the European emergency response community to develop sophisti-cated decision support systems that concentrate on long-range atmospheric transport and dispersion
modeling. On the other hand, since the accident at Three Mile Island, numerous changes have been made to off-site short-range dose models in order to overcome numerous difficulties relating to unreliabil-ity, speed, and operator interface. To improve the safety level, many users have recently gone back to the more basic simulation models that are easy to use but that produce overly conservative results. Some air quality simulation models can be used to aid in the predictions of impact levels within the impact zone at different time scales. They can also be employed to help identify the actual needs of siting those moni-toring stations indirectly.
At present, the AIRDOS-EPA computer model implements a steady-state Gaussian plume atmospheric dispersion model to calculate concentrations of radio-nuclides in the air and on the ground. It also uses US Nuclear Regulatory CommissionÕs (NRC) Regulatory Guide 1.109 food chain models to calculate radionu-clide concentrations in foodstuffs (vegetables, meat, and milk) and subsequent intakes by humans (US EPA 1979). In addition, there are three popular US. EPA air quality and air dispersion models, including ISCST3, AERMOD, and ISC-PRIME. The ISCST3 is a Gaussian plume model and is widely used to assess pollution concentration and/or deposition flux on receptors from a wide variety of sources. AERMOD is the next-generation air dispersion model that incorporates planetary boundary layer concepts. The ISC-PRIME model is similar to the ISCST3 model, but the ISC-PRIME model has been designed to incorporate the two fundamental features associated with building downwash: enhanced plume dispersion coefficients due to the turbulent wake, and reduced plume rise caused by a combination of the descending streamlines in the lee of the building and the increased entrain-ment in the wake (Schulman and others 1999). ISC-PRIME explicitly treats the stack location with respect to the building, the influence of streamline deflection on plume trajectory, the effect of wind angle on wake structure, and the effect of plume buoyancy and verti-cal wind speed shear on plume rise near buildings. Because this study focuses on airborne radionuclide monitoring, the ISC-PRIME model will eventually be adopted to simulate the diffusion, dispersion, trans-port, and transformation process of airborne radio-nuclides emitted from the nuclear power plant of concern.
A normal design scheme for siting the monitoring stations is to divide a study area into a continuous grid system with an equal grid size in which each grid rep-resents a candidate site in the network. The simulation analysis selected for this study was conducted in a study
area of 15 km · 17 km around the Maanshan plant, in which there are 212 computational grids, each with a size of 1 km · 1 km. The time period T is 1 year in this study because the simulation analysis was carried out based on a 1-year emission inventory and meteorolog-ical database, collected by the Taiwan Power Company in 1998. The concerned radionuclides in simulation analysis are shown in Table 2. The records indicates that there are four types of radiation emission: (1) fission and activation gases, (2) radioactive iodine, (3) particles, and (4) tritium. Most doses associated with radionuclide releases to the environment are caused by interactions between radiation emitted and human tissue accepted. These interactions involve the transfer
of energy from the radiation to the tissue, which is a process that might damage the tissue. The radiation might come from radionuclides located in or on envi-ronmental media or objects or from radionuclides deposited inside the body by inhalation, ingestion, and absorption through the skin. Hence, environmental concentrations and doses to people from airborne re-leases of radionuclides can be estimated through the application of the dose conversion factor (DCF), as indicated in Table 3, where immersed dose, inhalation dose, and exposure from deposited radionuclides have been taken into account. To convert dose rate to activity, the following equation can be applied (US EPA 1993):
Figure 3. The analytical framework of this study.
Dose rate ¼Dose conversion factor
Activity Density of media Time:
In principle, radiation caused by different types of radionuclide might exhibit quite a different exposure timescale. It is conceded that only 4 days integration time is to be taken for the dose in exposure assessment of all radionuclides in this study for the purpose of demonstration. During the simulation time period, the meteorological monitoring stations provide the data-base with wind speed, wind direction, stability class, and height of mixing layer required for tracing pollu-tant dispersion, transport, and transformation on an hourly basis. Figure 4 presents both the seasonal and annual wind rose diagrams in southern Taiwan. The wind speed and wind direction vary over seasons; however, the northeast, north-northeast, and east wind are the dominant wind directions over the entire year. The meteorological measurements provide the driving force in the simulation model. Characterization of the radiological consequences of radionuclides released in the atmosphere from the Maanshan plant operations during 1998 was accomplished by calculating, for each type of emission and for the entire dosage possibilities, the maximally exposed off-site individuals and the en-tire population residing within 50 km of the center of the plant. The effective dose equivalent (EDE) was also applied for assessing a risk-based dose equivalent that
can be used to estimate health-effect risks to popula-tion exposed in the study area on an annual basis.
Multiobjective Evaluation Analysis
The design procedure needs to identify several sig-nificant planning objectives and consider a series of inherent constraints simultaneously. The Committee of Industrial Safety and Hygiene in the power plant joined the selection of the planning objectives. Three objectives considered in this analysis were (1) the maximization of detection capability of the highest environmental concentration of radiation, (2) the maximization of detection capability of the highest frequency of violation, and (3) the maximization of population coverage. However, the choice of multiple-objective functions here is not meant to straddle dif-ferent possible goals of the monitoring system. For instance, one might want more monitoring in areas where evacuation or sheltering might be more likely to go wrong. One might want more monitors in areas with a higher percentage of children (e.g., near schools). One might want to choose monitors so that one could use a computer model to best predict concentrations/ exposures everywhere. In other words, it might be useful to add an objective function that reached high values when the data from a monitor deployment gave best average backfit to the release. Presumably, each planning scenario designed for different power plant might have differing objective functions. The formu-lation here is using the linear objective function to screen an infinite number of choices.
Hence, a multiobjective programming model is de-signed as a screening tool to pick up the most appro-priate subset within the proposed continuous grid system so that the design objectives can be illuminated and compromised by each other with respect to the preference weight while budget and spatial correlation constraints can be confirmed. Each grid defined in the study area is thus equivalent to a candidate site waiting for the possible selection in the multiobjective trade-off process. If the first objective can be maximized on its own, all of the sites would go to the region(s) where average concentration is highest. Maximizing other objective functions, presumably, will pull some of the locations away from the maximum average concentra-tion. Different objectives thus offer different driving forces that actuate the trade-off along the line. In addition, spatial correlation among paired candidate sites has to be evaluated before the analysis is per-formed. This information to be embedded in the multiobjective evaluation scheme implies that the higher the spatial correlation, the less the chance for Table 2. The concerned radionuclides in simulation
analysis in 1998
Classifications Radionuclide Activity (Bq) Fission and activation gases Ar-41 1.92E + 12
Kr-87 3.02E + 07
Xe-133 9.03E + 10 Xe-135 8.44E + 09 Xe-135m 4.63E + 08 Xe-138 2.69E + 07
Radioactive iodine I-131 1.28E + 02
I-133 6.36E + 02 Particle Cr-51 6.77E + 06 Mn-54 4.44E + 05 Co-57 6.88E + 04 Co-58 2.33E + 07 Co-60 2.17E + 06 Fe-59 2.67E + 05 Nb-95 1.24E + 06 Sn-113 5.29E + 04 Zn-65 1.06E + 05 Zr-95 8.81E + 05 Sr-89 1.22E + 01 Sr-90 1.69E + 01 Tritium H-3 4.63E + 12
two sites to be simultaneously considered as monitor-ing sites. Final sitmonitor-ing alternatives or relocation strate-gies can then be evaluated and determined with respect to several planning scenarios.
The objective function and constraints set below are to be sequentially defined in the following subsections.
Objective Functions
The objective function and constraints prepared to achieve such planning goals can be stated as follows: 1. Maximization of detection capability of the highest
environmental concentration. This consideration implies that the higher the environmental con-centration of radiation, the larger the possibility for a grid to be picked up around the nuclear power plant. It can be expressed as
Z1¼
XN j¼1
ðCjYjÞ ð1Þ
in which Z1 is the aggregated average
environ-mental concentration of radiation over the simu-lated region in the whole year (lSv/year or mBq/ m3). Cjis the average environmental concentration
of radiation at grid j, simulated by the ISC-PRIME model (lSv/h or mBq/m3). Yjis the binary integer
variable; it is equal to 1 if the grid i is selected as a monitoring station, 0 otherwise (unitless). N is the total number of grids divided in the study area (unitless).
2. Maximization of detection capability of the highest frequency of violation: This is another consider-ation relevant to the dosage impact, which implies that the higher the frequency of violation, the lar-ger the dosage impact would appear in a region. This is obtained by
Z2¼
XN j¼1
ðDjYjÞ ð2Þ
in which Z2 is the total numbers violating the
threshold limit value. The threshold limit value was selected in accordance with ‘‘The Safety Standard for Ionizing Radiation Protection in Taiwan’’ (1991). The values are 0.5 lSv/year for TLD and 90 mBq/m3 for AP. Dj is the frequency of violation
being detected or predicted at grid j (unitless). This number is related to the assumed release magnitude. Yet, the frequency of exceeding will Table 3. The dose conversion factor for the various exposure pathways
Classifications Radionuclide
Dose Conversion Factor (DCF)a
Immersion in contaminated air
Inhalation (lung class)
4-day exposure to gamma-radiation from deposited radionuclide
Fission and activation gases Ar-41 — — — Kr-87 5.1E + 02 — — Xe-133 2.0E + 01 — — Xe-135 1.4E + 02 — — Xe-135m 2.5E + 02 — — Xe-138 7.1E + 02 — —
Radioactive iodine I-131 2.2E + 02 3.9E + 04(D) 1.3E + 04
I-133 3.5E + 02 7.0E + 03(D) 7.3E + 03
Particle Cr-51 — — —
Mn-54 5.0E + 02 8.0E + 03(W) 3.3E + 03
Co-57 — — —
Co-58 5.8E + 02 1.3E + 04(Y) 3.8E + 03
Co-60 1.5E + 03 2.6E + 05(Y) 8.9E + 03
Fe-59 7.0E + 02 1.8E + 04(D) 4.2E + 03
Nb-95 4.5E + 02 7.0E + 03(Y) 2.9E + 03
Sn-113 4.8E + 00 1.3E + 04(W) 5.9E + 01
Zn-65 3.4E + 02 2.4E + 04(Y) 2.1E + 03
Zr-95 4.3E + 02 2.8E + 04(D) 2.9E + 03
Sr-89 8.2E + 02 5.0E + 04(Y) 5.2E) 01
Sr-90 0.0E + 00 1.6E + 06(Y) 0.0E + 00
Tritium H-3 0.0E + 00 7.7E + 01(V) 0.0E + 00
aunit of DCF: rem per lCi/cm3h
change, if the release magnitude changes. If there is more than one threshold limit value to consider, we might have one limit value for early health ef-fects or another level focused on a de minimus risk of cancer so that the resulting optimized network might be affected depending on which aggregate threshold value s considered. Presumably, analysts should pick the most restrictive one. In this study, for the purpose of demonstration, this parameter value was decided by the ISC-PRIME simulation model based on a source term that existed in the regular operational period of the power plant. 3. Maximization of population coverage. Equity
con-cerns with regard to such an event in this article could be that neighborhoods with higher pollution potentials or risks do bear a disproportionate share of environmental impacts. Hence, the corre-sponding population density in each grid around a nuclear power plant should be taken into account through a locational strategy of monitoring stations deployment. This can be expressed as
Z3¼
XN j¼1
ðPjYjÞ ð3Þ
in which Z3 is the total population that can be
serviced by the designed monitoring network. Pjis
the population that can be serviced if grid j in the area is selected as a monitoring station (capita/ km2). N is the total number of grid divided in the study area (unitless).
The final objective function is then given by a weighted approach:
maxX
3
i¼1
WiZi
in which Wi are the preference weights to be
adopted in decision analysis. Constraint Set
The constraint set defined in this analysis covers the cost and the efficiency criteria in the trade-off process. The cost criterion is described through stipulated budget constraints and the efficiency criterion can be illustrated by spatial correlation and concentration differentiation constraints, exclusively in the decision analysis. They are described as follows:
1. Budget constraint. This constraint limits the num-ber of monitoring station that can be selected in the optimization process, defined with respect to budget limitations.
XN j¼1
Yj B
in which B is the upper bond of the number of monitoring stations (unitless).
2. Spatial correlation constraint. This constraint guarantees that the required number of monitor-ing stations in the network depends on not only the spatial correlation coefficient Rjkbut also the cutoff
value of the spatial correlation coefficient Rc. The
spatial correlation between grids j and k could be represented by the spatial correlation coefficient, Rjk, and it was defined as (Modak and Lohani,
1985a) Rjk¼ PT t¼1 ½ðCtj CjÞ ðCtk CkÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PT t¼1 ðCtj CjÞ2P T t¼1 ðCtk CkÞ2 s 8jðj 6¼ kÞ ð5Þ in which Ctj or Ctkis the pollutant concentration
measured at grid j and time t or at grid k and time t, respectively (lSv/h or Bq/m3). Cj or Ck is the
average environmental -concentration of radiation measured at grid j or k within the time period T (i.e., 1 year in this study), respectively (lSv/h or Bq/m3). Such a consideration would enable us to focus on the selection of those grids with higher differentiation potentials in terms of exposure assessment. Therefore, the spatial correlation con-straint could be defined as
RjkðYjþ YkÞ 2Rc 8j; k ðj 6¼ kÞ ð6Þ
in which " stands for the implication of ‘‘for all’’ in mathematics. Rc is the cutoff value of the spatial
correlation coefficient. It provides a clue that the model will reject grid locations that fail to meet a threshold criterion. This implies that when the spatial correlation coefficient of two candidate sites for monitoring exceeds the threshold value, the two sites should not to be selected simultaneously. Such a threshold value is therefore tied in with source terms, wind field pattern, topography, and the features of pollutants. It means the summation of Yjand Ykin Equation 6 will never equal 1 if Rjkis
larger than 2Rc.
The cutoff value Rc is a system parameter to be
determined by decision-makers or planners prior to the analysis. The monitoring network with a higher Rc-based parameter value should have a larger
other hand, the monitoring network with a lower Rc-based parameter value should provide us with a
higher effective coverage area in an optimized network. Rcis the only parameter that can cause the
number of monitors after optimization to be less than the maximum number in the constraint. Depending on Rc, one could end up with fewer sites
that meet the spatial constraint than allowed in the budget. Given the stipulated budget in Equation 4, it would become the subjective determination of the power plant whether it should maintain either a higher or a lower Rc-based monitoring network.
However, 0.9 was applied as the Rc value in this
study in order to maintain as many monitoring stations as possible within the budget limitation so as to increase the public acceptance from a societal point of view.
3. Non-negativity constraint. All of the binary decision variables (Yj) are defined as non-negative.
Preference Weights Determination
Combining multiple objectives into a decision arena in the multiobjective decision-making process requires executing further decision analysis to extract the pref-erence weights from a group of domain experts, which are needed to aid in the trade-off procedure. A two-stage analysis employing a questionnaire survey in the first stage and a goal-programming analysis in the sec-ond stage would be able to help extract the preference weights.
Goal programming is a method that attempts to minimize the set of deviations from prescribed multi-ple goals, which are considered simultaneously and are weighted according to their relative importance (Zeleny 1982). It is known that a nonpreemptive goalprogramming technique is capable of investigating the preference weights with respect to a set of desig-nated planning objectives (Ning and Chang 2002). Nonpreemptive goal programming means that all goals are of roughly the same importance in decision-making so that there is no hierarchical structure that needs to be taken into account. This implies that these three monitoring networks at three existing nuclear power plants are of roughly comparable importance. With a nonpreemptive goal-programming model in the sec-ond stage, the implicit preference weights can be elic-ited from the questionnaire outputs when knowledge of how these domain experts take those objectives into account separately is apparent with respect to a series of evaluation criteria (i.e., the planning objectives here) in the first stage. Overall, a group of domain
experts is grading an existing set of three power plants. Questionnaire lists all ranking scores in a 3 · 3 matrix individually. Then extraction of preference weights from the matrix can be performed after the review committee eventually prioritizes the average ranking through group decision-making.
Questionnaire Investigation
The planning objectives considered in this analysis are designed to address the detection capability for highest environmental concentration; to enhance the detection capability of highest frequency of violation; and to reflect the protection capability of highest population coverage. Three existing nuclear power plants in Taiwan have been selected as a group of candidates for further assessment of how well those monitoring stations are sited with respect to three designated planning objectives. With a questionnaire designed explicitly for eliciting the performance of existing networks, domain experts in the field of radi-ation protection and environmental management in-vited to form a review committee were requested to grade the monitoring system situated in each power plant sequentially using the objectives. Therefore, the outputs of the questionnaire can be presented by a 3 · 3 matrix that provides the clues of preference weights to be extracted in the follow-up step of goal program-ming. The possible range of the grade should be de-fined in advance in order to have a set of more consistent outputs (Ning and Chang 2002). Until all similar monitoring systems under evaluation have been graded, all experts in the evaluation committee have to proceed with an overall justification regarding the integral performance of each system subjectively. Stakeholders with strong domain knowledge and/or local social contact were invited to join the committee. Final consensus must be made by the evaluation com-mittee to pinpoint exactly which monitoring project is better than the others in a logical sense so that an overall ranking (i.e., priority list) can be produced for subsequent goal-programming analysis. Based on the outputs, with respect to each objective and the integral evaluation, the final assessment is to apply an optimi-zation analysis. Extraction of preference weights from the matrix systematically can then be achieved in the next step.
Non Preemptive Goal-Programming Analysis The approach used to elicit the preference weights was based on a nonpreemptive goal-programming analysis. In the first stage, all three existing nuclear power plants in Taiwan are subjective to a holistic re-view by domain experts separately with respect to a set
of criteria, and then collectively in order to determine the overall ranking among these three mentoring networks. Because the goal-programming model was designed for the decision of preference weights asso-ciated with the planning objectives, the objectives dis-cussed in the first stage are the same ones as mentioned earlier in the multiobjective evaluation model. In the goal-programming model, however, the goals to be judged are those overall rankings priori-tized by the domain experts, which form a set of targets to be achieved via the minimization of overall devia-tions from their aggregate target values. The model formulation is as follows (Ning and Chang 2002). Equation 7 minimizes the total deviation derived from the final consensus presented by the review committee (domain experts) over these three operational nuclear power plants. Equation 8 describes the consensus of prioritization among these three nuclear power plants finalized by the review committee. Equation 9 ensures that the disparity between preference weights should not be too large. The bridge in between stage 1 and stage 2 is the determination of the overall ranking by the review committee. The target value in the goal-programming model is thus derived in conjunction with Equation 8. The preference weights can be determined by such an optimization analysis that can be solved by some software packages, such as LINDO.
minX m j¼1 ðdiþþ diÞ ð7Þ Subject to: Xm j¼1 WjGi;jþ did þ i Xm j¼1 WjGiþ1;jþ diþ1 d þ iþ1 ð8Þ " the ith
project is better than the (i + 1)thproject
Wj Wmin 8j ð9Þ
Gi;j; diþd
i 0 8i; j ð10Þ
where the subscript i represents the numeric order of objectives considered in the model (unitless), m is the total number of objectives included in the model, and dþi and di are the unitless positive and negative devi-ational variables, respectively, that describe the degree of distance from a selected target value. These two decision variables are mutually exclusive in a logical sense; therefore, the multiplication of them should be equal to zero (dþi; di 0 8i; j). Wj represents the
preference weight of the jth objective (decision vari-able) (unitless), Gi,j is the mean score of the jth
objective assigned by domain experts when assessing the ith similar project (unitless), and Wminis the
min-imum value of the preference weight required in the weight-matching process (unitless). In this study, it was set as 0.1 because decision-makers did not want to abandon any planning objectives.
Results and Discussion
Preference Weights Determination
To gain a comprehensive solution, a goal-program-ming model was formulated to identify the preference weights associated with the planning objectives men-tioned earlier when considering the relocation possi-bilities of these monitoring stations. The database obtained from eight questionnaires was used in a goal-programming model to elicit the final preference weights for all objectives. Table 4 presents the mean scores with respect to each objective associated with the three nuclear power plants selected in this survey. The tabulated values only list the 4-day period of exposure. Additionally, the final consensus with regard to the integral evaluation for the three existing nuclear power plants include the following: (1) The second plant is generally better than the first plant; (2) the second plant is generally better than the third plant; and (3) the third plant is generally better than the first plant.
Such a technical setting would enable us to preserve the minimum significance of each planning objective considered in this survey. Otherwise, some of the objectives might be excluded in the trade-off process because of an extremely low weighting factor. The goal-programming model finally yields a set of normalized preference weights. They are 0.7, 0.1, and 0.2 for planning objective 1, 2, and 3, respectively. Such an algorithm would enable us to link the fragmented information of each domain expertÕs individual score associated with each monitoring project and extract and elicit the implicit preference weights embedded in expertsÕ overall ranking after making an integral eval-uation in the end. This approach might exhibit a set of Table 4. Mean scores (Gi, j) of questionnaire Plant No. Objective 1 Objective 2 Objective 3(1)
1 6.6 6.9 7.7
2 7.0 7.6 9.3
3 7.7 7.7 6.7
Note: Objective 1: the maximization of detection capability of highest environmental concentrations of radiation; objective 2: the maximi-zation of detection capability of highest frequency of violation; objective 3: the maximization of protection capability of highest population density.
more consistent outputs rather than taking a straight-forward mean score into account.
Simulation Analysis
The ISC-PRIME model has been used to simulate the diffusion, dispersion, transport, and transportation process of radionuclides emitted from a nuclear power plant in this study. Figures 5 and 6 show the contour maps of simulated annual average concentration with direct radiation dosage and gross beta activity, respec-tively, in the study area. The highest concentration occurred in the inner part of the nuclear plant. The adjacent regions, the south, west, and southeast areas, present the relatively highest dosage or activity of radiation. The higher concentration in the west area is due to the prevailing wind direction in this region. The occurrence probability of an east wind is about 13% over the whole year, as indicated in Figure 4. However, the prevailing wind, from northeast and north-north-east directions, does not cause any higher concentra-tion in the leeward direcconcentra-tions. That is due to local topography. The higher terrain (about 50–100 m) southeast of the nuclear power plant drives the wind from northeast and north-northeast to north in direc-tion and forms a local circuladirec-tion pattern in the south
direction, consequently increasing the odds of a higher concentration in the south sides of the plant.
Multiobjective Evaluation Analysis
There are four sets of planning scenarios being or-ganized based on different combinations of decision weights associated with prescribed budget limitations (see Table 5). The group ‘‘a’’ designation refers to equal weights and the group ‘‘b’’ refers to the inclu-sion of preference weights as derived earlier (i.e., 0.7. 0.1, and 0.2). The cases with equal weight are designed as the base cases for comparison purposes. Varying numbers of monitoring stations available have been assigned in different planning scenarios that reflect the cases of budget limitation. Some of them have had identical weights applied, and the others employed the preference weights in accordance with the goal-pro-gramming outputs. The corresponding mixed-integer programming models defined for those scenarios have been solved by the software package ILOG CPLEX 7.1. Figures 7–10 demonstrate the spatial distribution of those monitoring sites selected by the optimization model.
The conflict and compromise among these three planning objectives are obvious because the first and TLD308 TLD309 TLD310 TLD311 TLD312 TLD313 TLD314 TLD319 TLD320 TLD321 TLD322 TLD323 TLD324 TLD325 TLD326 TLD327 TLD328 TLD329 TLD330 TLD331 TLD332 TLD333 TLD335 TLD336 TLD337 TLD339 TLD340 216000 218000 220000 222000 224000 226000 228000 230000 TM2-E (m) 2424000 2426000 2428000 2430000 2432000 2434000 2436000 2438000 2440000 TM 2 -N ( m ) 0.00E+000 6.25E-009 1.25E-008 2.50E-008 5.00E-008 1.00E-007 2.50E-007 5.00E-007 6.50E-007 8.00E-007 mSv/yr
Figure 5. The simulated annual average concentration distribution of direct radiation dosage in the study area.
second objectives try to emphasize the detection capability of higher environmental concentration and frequency of violation in the west and south area; however, the third objective focuses on the protection of the highly populated areas in the northeast and southwest regions. When the upper bound of the total number of monitoring stations is set as 5, the prefer-ence weights would deeply affect the choice of candi-date sites 12 and 98, as indicated in cases 1(a) and 1(b). For example, the scenarios with unequal pre-ference weights associated with objectives may come up with a differing site selection strategy in which site 12 becomes favorable due to its environmental sensitivity. A similar situation appears in the trade-off process between sites 73 and 58, as evidenced by cases 3(a) and 3(b). When the upper bound of the total number of monitoring stations is set at 10 or 27, the preference weights will not affect the planning outcome too much, as indicated in cases 2(a), 2(b), 4(a), and 4(b). Only 24 candidate sites have been selected in the optimization process, even though the upper bound of the total number of monitoring stations is set at 27 in case 4(a) and (b). The results mean that only 24 candidate sites could satisfy the requirements of constraints. It implies that 24 monitors might be the maximum number of installation stations under the technique setting in this
study. The critical factor is the spatial correction restriction. Loosening or tightening the threshold value would also change the planning results. No matter how many sites might be picked for monitoring in a particular scenario, the lower the total number of monitoring stations allowed, the more chances for the model to pick those candidate sites located at the southwest part of the nuclear power plant that is closer to the populated region. The outcome shows that the weights associated with planning objectives did not obviously dominate the choice of monitoring stations. This means that the constraints are relatively strict, so the space for trade-off between objectives is limited to some extent.
A relocation strategy for TLD and AP monitoring networks has been suggested in this study. It is based on the planning results of case 4(b). For 27 existing TLD monitoring stations, 10 stations are retained, 14 stations need to be moved out to the neighboring sites, and 3 stations could be discarded. Figure 11 delineates the relocation strategy as a whole. On the other hand, for 22 existing AP monitoring stations, 8 stations are retained, the other 14 stations need to be moved to the neighboring sites, and 2 new stations are required for improving the effectiveness of monitoring. Figure 12 describes the relocation strategy as a whole.
216000 218000 220000 222000 224000 226000 228000 230000 TM2-E (m) 24240 00 24260 00 24280 00 24300 00 24320 00 24340 00 24360 00 24380 00 24400 00 TM2-N (m) AP301 AP302 AP303 AP304 AP305 AP306 AP307 AP308 AP309 AP310 AP311 AP312 AP313 AP314 AP315 AP316 AP317 AP318 AP319 AP321 AP322 AP323 0.00E+000 2.50E-005 5.00E-005 1.00E-004 2.00E-004 5.00E-004 1.00E-003 2.00E-003 3.00E-003 4.00E-003 mBq/m3
Figure 6. The simulated annual average concentration distribution of gross beta activity in the study area.
Overall, the resulting network might end up not doing very well in any of the chosen areas. Perhaps, it will end up doing well in one category of planning objective in one region and another categoryin an-other area. This is due to an inherent difference be-tween single-objective and multiobjective programming. In a multiobjective problem, the con-flicts between objectives are inevitable in the sense that the final optimized network would not be the optimal solution associated with any single objective. It is a compromised solution. However, we could adjust the preference weights of planning objectives or increase constraints to emphasize or limit individual objectives. We also could build the monitoring network by con-sidering the single objective one at a time and combine all of the results eventually; however, it is obvious that they would not be the all-embracing outcomes.
Overall, the benefit generated by the model is actually embedded in the relocation strategies of those monitoring stations. They could be closer to the pop-ulation center after relocation so that the societal benefit can be enlarged. It is expected that the total risk of cancer and total number of early deaths or injuries should be reduced if the total population dose can be minimized to some extent. This is also the im-plicit goal of the experts from whom the authors elic-ited preference weights. The end goal of this study was to provide a set of relocation strategies that might re-duce the total number of stations, on one hand, and make the optimized network closer to the prescribed objectives, on the other hand, so as to support a better monitoring capacity and a more informed emergency response plan when triggering for evacuation.
Conclusions
This study focuses on assessing the radioactive pol-lution impact to the atmospheric environment from a nuclear power plant located at the southernmost coastal plain in Taiwan. By conducting an integrated simulation–optimization study, the relocation strate-gies of two types of monitoring system can be explored within a consolidated network. The ISC-PRIME model in the first stage was employed for generating the essential background information required in the subsequent multiobjective evaluation analysis. In par-ticular, three planning objectives for the minimization of the impacts of highest environmental concentra-tions, the highest frequency of violation, as well as the maximization of population coverage were emphasized subject to budget and spatial correlation constraints. The case study assessed for a nuclear power plant
lo-Table 5. Technical setttings and planning results Weightings Total no. of Siting alternative candidate Scenarios W1 W2 W3 monitoring stations locations (see Figures 7 – 10) Case (1a) 1 1 1 5 21, 22, 32, 33, 98 Case (1b) 0.7 0.1 0.2 5 12, 21, 22, 32, 33 Case (2a) 1 1 1 1 0 12, 20, 21, 22, 23, 32, 33, 44, 45, 98 Case (2b) 0.7 0.1 0.2 10 12, 20, 21, 22, 23, 32, 33, 44, 45, 98 Case (3a) 1 1 1 1 5 3 , 12, 20, 21, 22, 23, 32, 33, 44, 45, 46, 47, 48, 73, 98 Case (3b) 0.7 0.1 0.2 15 3, 12, 20, 21, 22, 23, 32, 33, 44, 45, 46, 47, 48, 58, 98 Case (4a) 1 1 1 2 7 1 , 3 , 12, 20, 21, 22, 23, 25, 32, 33, 44, 45, 46, 47, 48, 53, 58, 70, 73, 98, 105, 107, 131, 186 Case (4b) 0.7 0.1 0.2 27 1, 3, 12, 20, 21, 22, 23, 25, 32, 33, 44, 45, 46, 47, 48, 53, 58, 70, 73, 98, 105, 107, 131, 186
cated at Hengchun Peninsula, southern Taiwan illu-minates such an application potential. With a non-preemptive goal-programming model, the implicit decision weights can be elicited from the questionnaire outputs. Yet, the preference weights of planning objectives would not obviously dominate the choice of
monitoring stations in the end. Given the assumption that evacuation times are the same in all directions, the evacuation actions, as part of the emergency response, can then be handled by the power plant by referring to the on-site and off-site monitoring records simulta-neously.
Figure 8. Planning results of cases 2(a) and 2(b). Figure 7. Planning results of cases 1(a) and 1(b).
However, the lower-bound limitation of the num-ber of monitoring stations was not included in this study because budget constraint is not so critical in the screening process. Yet, there is a need to evaluate such an impact if the budget is really tight. On the
other hand, the larger the total number of monitoring stations we would like to deploy, the higher the safety the society might acquire from the psychological point of view. The upper and lower bounds of the total number of stations could also be tied in with the Figure 9. Planning results of cases 3(a) and 3(b).
minimum level of acceptable risks. Because the acceptable risks can hardly be justified quantitatively, this analysis only takes the upper bound into account. This model is designed to consolidate the monitoring network for both TLD and AP systems; yet, the TLDs and APs might require different choices of spatial correlation cutoff and threshold detection limits and therefore end up with different numbers and be lo-cated in different places, if necessary in future study. Assuaging public concern might dictate redundancy of monitors that might be considered in each candi-date site based on the final suggestions for relocation if the management agency has a secondary budget. Based on such a systematic assessment, final sugges-tions might satisfy part of the practical needs of decision-making with regard to how to simultaneously reduce the total number of monitoring stations and meet the requirements of monitoring objectives in this power plant. However, a stochastic multiobjective programming model might be used in the future to address the probability of monitor failure in
con-junction with more than one threshold limit value for an advanced study.
Acknowledgments
The authors acknowledge the data reports cited and used in this study and the helpful comments provided by all anonymous referees.
Appendix 1. Notation
Cj The average environmental concentration of
radia-tion measured or predicted at grid j within the time period T (lSv/h or Bq/m3)
dþi;d
i The positive and negative deviational variables
for goal programming (unitless)
B The upper bound of the total number of monitoring stations (unitless) 1 3 12 20 21 22 23 25 32 33 44 45 46 47 48 53 58 70 73 98 105 107 131 186 216000 218000 220000 222000 224000 226000 228000 230000 TM2-E (m) 2424000 2426000 2428000 2430000 2432000 2434000 2436000 2438000 2440000 TM 2 -N ( m ) Case (4a) TLD TLD333 TLD332 TLD335 TLD337 TLD336 TLD319 TLD329 TLD331 TLD327 TLD323 TLD325 TLD320 TLD311
Figure 11. The suggested relocation strategy for the TLD monitoring network.
Cj; Ck The average environmental concentration of
radiation measured at grid j or k within the time period T, respectively (lSv/h or mBq/m3)
Ctj, CtkThe pollutant concentration measured at grid j
and time t or at grid k and time t, respectively (lSv/h or mBq/m3)
Dj The frequency of violation being detected or
pre-dicted at grid j (unitless)
Gi,jThe score of the jth objective assigned by assessing
the ith similar project (unitless)
N The total number of grid divided in the study area (unitless)
PjThe population that can be serviced if the grid j in
the area is selected as the monitoring station (cap-ita)
Rc The cutoff value of spatial correlation coefficient
(unitless)
Rjk The spatial correlation coefficient between grid j
and grid k with respect to the concerned pollutant (unitless)
Wi The preference weights in decision analysis
(unit-less)
Wmin The minimum value of the preference weight
required in the weight-matching process (unitless) YjThe binary integer variable; it is equal to 1 if the grid
i is selected as a monitoring station, 0 otherwise (unitless)
Z1 The aggregated average environmental
concentra-tion of radiaconcentra-tion over the simulated region in the whole year (lSv/year or mBq/year)
Z2The total numbers of violating the threshold limit
value
Z3 The total population that can be serviced by the
designed monitoring network
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