Optimizing the spatial pattern of networks for monitoring radioactive releases

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.

[1]  Noel A Cressie,et al.  Spatial prediction from networks , 1990 .

[2]  Alfred Stein,et al.  Constrained Optimization of Spatial Sampling using Continuous Simulated Annealing , 1998 .

[3]  J. Eheart,et al.  Monitoring network design to provide initial detection of groundwater contamination , 1994 .

[4]  D. J. Brus,et al.  Sampling for Natural Resource Monitoring , 2006 .

[5]  Gerard B. M. Heuvelink,et al.  About regression-kriging: From equations to case studies , 2007, Comput. Geosci..

[6]  Jürgen Pilz,et al.  INTAMAP: The design and implementation of an interoperable automated interpolation web service , 2011, Comput. Geosci..

[7]  Dale L. Zimmerman,et al.  Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction , 2006 .

[8]  M. Stein,et al.  Spatial sampling design for prediction with estimated parameters , 2006 .

[9]  B. Hobbs,et al.  Review of Ground‐Water Quality Monitoring Network Design , 1993 .

[10]  R. Bilonick.  An Introduction to Applied Geostatistics , 1989 .

[11]  Gene H. Golub,et al.  Matrix computations , 1983 .

[12]  J. W. van Groenigen,et al.  Chapter 14 Designing Spatial Coverage Samples Using the k-means Clustering Algorithm , 2006 .

[13]  X. Wen,et al.  Geostatistical analysis of an experimental stratigraphy , 2005 .

[14]  Gerard B. M. Heuvelink,et al.  Optimization of sample configurations for digital mapping of soil properties with universal kriging , 2006 .

[15]  R. C. Smetsers,et al.  Variations in Outdoor Radiation Levels in the Netherlands , 1996 .

[16]  R. Smetsers,et al.  Source-Dependent Probability Densities Explaining Frequency Distributions of Ambient Dose Rate in the Netherlands , 1997 .

[17]  Peter M. Atkinson,et al.  Non-stationary variogram models for geostatistical sampling optimisation: An empirical investigation using elevation data , 2007, Comput. Geosci..

[18]  J. W. Groenigen,et al.  Constrained optimisation of soil sampling for minimisation of the kriging variance , 1999 .

[19]  Yvo S. Kok,et al.  Data assimilation, sensitivity and uncertainty analyses in the Dutch nuclear emergency management system: a pilot study , 2007 .

[20]  Hannes Kazianka,et al.  Copula-based geostatistical modeling of continuous and discrete data including covariates , 2010 .

[21]  Edzer J. Pebesma,et al.  Real-time automatic interpolation of ambient gamma dose rates from the Dutch radioactivity monitoring network , 2009, Comput. Geosci..

[22]  Bithin Datta,et al.  Optimal Dynamic Monitoring Network Design and Identification of Unknown Groundwater Pollution Sources , 2009 .

[23]  F. Steinhausler.  What It Takes to Become a Nuclear Terrorist , 2003 .

[24]  Philippe Lagacherie,et al.  Digital soil mapping : an introductory perspective , 2007 .

[25]  Jeffrey H. Gove,et al.  Spatial residual analysis of six modeling techniques , 2005 .

[26]  Miguel A. Mariño,et al.  Sampling Design for Contaminant Distribution in Lake Sediments , 1995 .

[27]  Patrick M. Reed,et al.  Striking the Balance: Long-Term Groundwater Monitoring Design for Conflicting Objectives , 2004 .

[28]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[29]  G. Heuvelink,et al.  Optimization of sample patterns for universal kriging of environmental variables , 2007 .

[30]  David E. Dougherty,et al.  Optimal groundwater management: 2. Application of simulated annealing to a field-scale contamination site , 1993 .

[31]  Gerard B. M. Heuvelink,et al.  Sampling Optimization Trade-Offs for Long-Term Monitoring of Gamma Dose Rates , 2008, ICCSA.

[32]  Werner G. Müller,et al.  Collecting Spatial Data: Optimum Design of Experiments for Random Fields , 1998 .

[33]  Dubois Gregoire,et al.  Automatic Mapping Algorithms for Routine and Emergency Monitoring Data , 2005 .

[34]  Shahrokh Rouhani,et al.  Resilience of a statistical sampling scheme , 1986 .

[35]  James V. Zidek,et al.  Designing environmental monitoring networks to measure extremes , 2007, Environmental and Ecological Statistics.

[36]  Edzer J. Pebesma,et al.  Multivariable geostatistics in S: the gstat package , 2004, Comput. Geosci..

[37]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[38]  Yingqi Zhang,et al.  Least cost design of groundwater quality monitoring networks , 2005 .

[39]  A. McBratney,et al.  Further results on prediction of soil properties from terrain attributes: heterotopic cokriging and regression-kriging , 1995 .

[40]  Panagos Panagiotis,et al.  The European Soil Database , 2006 .

[41]  D. J. Brus,et al.  Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion) , 1997 .

[42]  Gerard B. M. Heuvelink,et al.  Optimization of mobile radioactivity monitoring networks , 2010, Int. J. Geogr. Inf. Sci..

[43]  U. Stöhlker,et al.  Characterization of dose rate instruments for environmental radiation monitoring , 2007 .

[44]  E. D. Brill,et al.  A method for locating wells in a groundwater monitoring network under conditions of uncertainty , 1988 .