interpolation of radon concentrations using gis-based kriging and cokriging techniques

Interpolation of RadonConcentrations UsingGIS-Based Kriging andCokriging TechniquesDilip Varma Manthena, Akhil Kadiyala, and Ashok KumarDepartment of Civil Engineering, The University of Toledo, Toledo, Ohio 43606; [email protected](for correspondence)

Published online 23 October 2009 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ep.10407

INTRODUCTION

Radon (Rn) is a colorless, odorless naturally occur-ring radioactive, inert gas formed by radioactive decayof uranium in soil or rocks. It is the only gas compo-nent produced during uranium decay. The primarysource of Rn in Ohio is from fragments of the uranifer-ous Ohio Shale that have been incorporated into thetill and other glacial deposits by the glaciers [1]. Rn canalso be referred to as a complete carcinogen, becauseit alone can initiate, promote, and propagate cancer.The primary site of exposure to Rn for majority of thepeople is their home. The United States EnvironmentalProtection Agency (U.S. EPA) classifies Rn as a provenand very potent ‘‘Class A’’ carcinogen with an exposurethreshold limiting value of 4 picocuries per liter (pCi/L). Rn is the leading cause of lung cancer among non-smokers. The National Cancer Institute estimates thecancer deaths caused by exposure to Rn accountingfrom 15,000 to 22,000 per year in the United States(i.e., 9–14% of the total cancer deaths) [2]. However,the World Health Organization (WHO) recommendsthe reduction of threshold limit for Rn to 2.7 pCi/L (i.e.,one-third of current limiting value) that could doublethe number of homes needing Rn control systems [3].The U.S. EPA, along with many other state healthdepartments, and various health organizations havelaunched research efforts and are creating manyawareness programs to assess the risk associated with

Rn exposure and identify the appropriate remedialmeasures.

The Ohio Department of Health (ODH) is respon-sible for Rn outreach and education and Rn licensingin Ohio. The ODH sends Rn records to The Univer-sity of Toledo (UT) for maintaining the completeRn database for the State of Ohio. The ongoing Rnresearch program at UT includes analysis of the Rndata, identification of zip codes and counties withRn concentrations greater than 4 pCi/L, identificationof the best Rn system to reduce indoor Rn concentra-tions, and plotting different maps showing the distri-bution of Rn concentrations across Ohio. At UT, dif-ferent database management tools have been devel-oped by the Department of Civil Engineering that arebeing used to manage the Rn database [4–8]. Kumaret al. [9] discussed in detail about the Rn researchbeing carried out at UT. Adopting the WHO guide-lines for Rn would certainly increase the number ofzip codes in Ohio that will require attention of thepublic as well as the ODH.

Figure 1 presents the geometric mean (GM) of Rnconcentrations available for each zip code in Ohio.Different colors in the map represent the varying Rnconcentration levels. The white color represents thezip codes where no data are available, and the redcolor represents the zip codes having Rn concentra-tions higher than 10 pCi/L. The Rn concentrationsobtained for each zip code are representative of theGM of Rn concentrations from the home owners liv-ing in the respective zip code areas.

SOFTWARE REVIEWS

� 2009 American Institute of Chemical Engineers

Environmental Progress & Sustainable Energy (Vol.28, No.4) DOI 10.1002/ep December 2009 487

Rn can be measured using various devices, such ascharcoal canisters, alpha track, positive barrier, etc.Exposure to indoor Rn levels can be prevented byadopting appropriate methods, such as subslabdepressurization, drain tile depressurization, etc. It isnot feasible to collect Rn data in each and everyhouse in Ohio, as it is a laborious and time-consum-ing task. Therefore, in such cases where the data arenot available or not approachable, interpolation tech-niques, such as kriging, inverse distance weighted,and cokriging, could be used to estimate Rn concen-trations.

Rn database available at UT, collected from differ-ent Rn testing organizations, resulted in representa-tion of Rn data for 1066 zip codes until 2008. Thereare a total of 1862 zip codes in Ohio. Rn concentra-tions are estimated for the unknown zip codes usingkriging and cokriging interpolation techniques. Thisarticle compares geographic information systems(GIS)-based kriging and cokriging interpolation tech-niques to estimate Rn concentrations for unknownlocations in Ohio.

DATABASE DEVELOPMENT

Radon DataRn concentrations have been collected from vari-

ous commercial testing services, health departments,and university researchers. The initial database of50,000 Rn concentrations was prepared by Kumaret al. [4], and later on the details of the Ohio Rn In-formation System (ORIS) were published by Hey-dinger et al. [10]. This Rn database was extended to82,000 observations in 1996 and 1997. Sud [11]reported total observations of 80,436 in her thesiswhile analyzing Rn data. New data are added to the

Rn database year by year. The total database forhomes consists of 133,343 Rn measurements for 1590zip code areas in Ohio. Of the 1590 zip codes repre-sented in the data, 254 zip codes are provided withunknown county names, and so these zip codes werenot considered for estimation. Of the remaining 1336zip codes, 270 were not shown in the Ohio zip codesshape file collected from the ESRI website [12]. Fromthe Rn data set of 1590 zip codes, 1066 zip codes areused as inputs representing point source data in theinterpolation techniques.

Uranium DataUranium data were obtained from the map pub-

lished by Duval [13] as shown in Figure 2. The mapprovides uranium concentrations in Ohio’s soil zoneas measured from an airplane. A map of Ohio’s zipcode areas was drawn to the same scale and overlaidon the uranium map, which resulted in obtaining thecorresponding uranium concentrations for respectivezip code areas. Each line of this file contains the zipcode followed by three coded numbers representingmodal uranium concentration, maximum uraniumconcentration, and minimum uranium concentrations.

METHODOLOGY

The GM of Rn concentrations for each zip code iscalculated, and the calculated GM concentration datavalue is attached to the attribute table for respectivezip codes in the Ohio shape file. The zip codes withno Rn data are represented with ‘‘0.’’ Table1 repre-sents a sample of the data, where GM and arithmeticmean are attached to the zip code file. Using datamanagement tools available in GIS, the polygon fea-tures of the Ohio zip codes shape file are convertedinto point features. These point features are used in

Figure 1. Geometric mean of indoor radon concentrations in Ohio zip code areas. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com.]

488 December 2009 Environmental Progress & Sustainable Energy (Vol.28, No.4) DOI 10.1002/ep

the interpolation techniques to estimate the Rnconcentrations. The point feature shape file is thenfurther divided into two shape files, with one shapefile having zip codes with Rn concentrations, that is,the 1066 zip codes, and the other shape file having796 zip codes with no measured Rn concentrationdata.

Geostatistical AnalystArcGIS Geostatistical Analyst can be used to

explore data variability, look for data outliers, exam-ine global trends, and investigate spatial autocorrela-tion and the correlation between multiple data sets. Itcreates prediction, prediction standard errors, theprobability that specified threshold was exceeded,and quantile maps using various geostatistical modelsand tools. Geostatistical interpolation technique isbased on statistics, which not only produce predic-tion surfaces but also error and uncertainty of surfa-ces. The interpolation techniques also provide theuser with the quantile and probability output maps.

KrigingKriging is a geostatistical interpolation technique

used to interpolate the value of a random field (e.g.,the elevation, z, of the landscape as a function of thegeographic location) at an unobserved location from

observations of its value at nearby locations. Thesemethods not only produce prediction surfaces butalso error or uncertainty surfaces. Kriging mainly per-forms two different functions: predicting and quanti-fying the spatial structure of the data. Kriging usesthe fitted model from variography to make a predic-tion for an unknown value of a specific location. Var-iography is nothing but quantifying the spatial datastructure. Kriging model interpolates with spatial dataconfiguration and the values of measured samplepoints around the prediction location. Geostatisticalanalyst provides many tools and defaults which helpin determining the parameters to be used, so that asurface can be created quickly. The kriging method isbased on the autocorrelation of Rn concentrationsbetween two points. The kriging model assumes themodel as in Eq. 1

ZðsÞ ¼ mðsÞ þ eðsÞ; (1)

where Z(s) is the variable of interest, decomposedinto a deterministic trend m(s) and a random autocor-related errors form e(s).

The symbol ‘‘s’’ denotes the location. One canthink of it as containing the spatial x- (longitude) andy- (latitude) coordinates. Some assumptions madeabout the error term e(s) are one would expect themto be 0 (on average) and that the autocorrelationbetween e(s) and e(s + h) does not depend on theactual location ‘‘s,’’ but only the displacement ‘‘h’’between the two. As m(s) is a deterministic trend, theselection of a kriging method is based on whether adirectional trend exists or not. Ordinary kriging wasselected to map the Rn concentration distributions.

Ordinary kriging assumes the model as in Eq. 2

ZðsÞ ¼ mþ eðsÞ; (2)

where m is an unknown constant.The ordinary kriging formula in general is given

by Eq. 3

Z�ðuÞ ¼XnðuÞ�¼1

��ðuÞZðu�Þ þ 1�XnðuÞ�¼1

��ðuÞ" #m

; (3)

where Z*(u) is the ordinary kriging estimate at spatiallocation u, n(u) the number of data points used atthe known locations given a neighborhood, Z(u�) then measured data at locations u� located close to u, mthe mean of distribution, and ��(u) is the weights forlocation u� computed from the spatial covariance

Table 1. Radon GM and AM added to Ohio shape file.

FID_OHZIP AREA ZIP PO_NAME STATE POP1999 FID_COUNTY COUNTY_NAM GM AM

0 20.66 43001 Alexandria OH 2088 44 LICKING 6.23 18.891 12.17 43002 Amlin OH 2221 24 FRANKLIN 9.90 14.321 12.17 43002 Amlin OH 2221 48 MADISON 0.00 0.001 12.17 43002 Amlin OH 2221 79 UNION 0.00 0.00

Figure 2. Aerial radiometric map of Ohio showing theuranium concentration in surficial sediments andsoils. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]


matrix based on the spatial continuity (variogram)model, which is given by Eq. 4:

�ðhÞ ¼ 1

2n

Xni¼1

ðzðuiÞ � zðui þ hÞÞ2; (4)

where n is the number of data pairs separated by dis-tance h, z(ui) and z(ui + h) are the data values atlocations separated by distance h.

Using the GIS-based geostatistical wizard tool,modeling is done for the whole Rn data set, whichcreates a surface of spatial variation of Rn concentra-tions. Predictions for unmeasured zip codes (whereno data are collected) are then evaluated from thesurface created and computed prediction errors.Figure 3 presents the spatial variation of the Rn con-centrations drawn using kriging interpolation tech-nique. The spatial surface shows that the Rn concen-trations are high in the central and west Ohio.

CokrigingCokriging interpolation technique uses multivari-

able data types for estimation. The main variable ofinterest is Z1, and both autocorrelation for Z1 andcross-correlations between Z1 and all other variabletypes are used to make better predictions. Cokrigingrequires much more estimation that includes estimat-ing the autocorrelation for each variable as well as allcross-correlations. Theoretically, when there is nocross-correlation, cokriging will autocorrelate for Z1.However, more variability is introduced each time toestimate unknown autocorrelation parameters so thatprecision of the prediction increases. The techniqueof simple cokriging has been found to give the mostreproducible estimations [14].

Ordinary cokriging assumes the models as inEqs. 5 and 6:

Z1ðsÞ ¼ m1 þ e1ðsÞ (5)

Z2ðsÞ ¼ m2 þ e2ðsÞ (6)

where m1, m2 are unknown constants and e1(s), e2(s)are random errors.

As there are two types of random errors, e1(s) ande2(s), there is autocorrelation for each of them andcross-correlation between them. Ordinary cokrigingattempts to predict Z1(s0) just like ordinary kriging,but it uses information in the covariate Z2(s) in anattempt to do a better job.

To predict Rn concentrations for the unknown zipcodes using the cokriging method, the model uses Rnconcentrations of the measured zip codes as theprimary data and the uranium concentrations as thesecondary data. As in the case of the kriging model,cokriging model also produces the surface variation ofRn concentrations, predicts concentrations of unmeas-ured zip codes, and computes prediction errors. Figure4 presents the surface distribution of Rn concentrationsin Ohio drawn using cokriging interpolation tech-nique. The spatial surface shows the Rn concentrationsto be higher in central and west Ohio regions as alsoobserved from kriging method.

Comparison of Kriging and Cokriging ModelsThe Rn concentrations for unmeasured zip codes

are obtained using kriging and cokriging models. Todetermine the better interpolation technique, predic-tion errors are derived for both the interpolation tech-

Figure 3. Spatial surface variation of radon concentra-tions obtained for Ohio using kriging interpolationtechnique. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]

Figure 4. Spatial surface variation of radon concentra-tions obtained for Ohio using cokriging interpolationtechnique. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]


niques. Figure 5 presents the comparison of predic-tion errors of kriging and cokriging interpolationtechniques. There are some differences among theprediction errors of the two interpolation techniquesadopted.

RESULTS

Cokriging interpolation technique estimates the Rnconcentrations of unmeasured zip codes using meas-ured Rn concentrations as primary data and the ura-nium concentrations as secondary data. This GIS-based interpolation technique not only estimates themissing Rn data but also predicts error and createsthe spatial surface variation of the Rn concentrations.By comparing the prediction errors of kriging andcokriging interpolation techniques, it was observedthat the cokriging interpolation technique producedminimal errors when compared with kriging interpo-lation technique (Figure 5). Even though there is notmuch difference in the prediction errors of the twotechniques adopted, cokriging interpolation tech-nique produced better results with less data. Theseresults are not given in this article.

CONCLUSIONS

This article demonstrates the use of two GIS-basedinterpolation techniques, kriging and cokriging, toestimate the Rn concentrations for unknown zipcodes in the State of Ohio. It was observed that cok-riging produced better results when compared withkriging. It was also observed that even for a lessernumber of known Rn concentrations than completedataset, cokriging interpolation technique still pro-duced better results. The spatial variation maps of Rn

concentrations plotted from kriging and cokriginginterpolation techniques (Figures 3 and 4) haveshown similar variation of uranium concentrationsin Ohio as observed from the aerial radiometric con-tour map of uranium concentrations of Ohio (Figure2), with higher concentrations in central and westOhio.

ACKNOWLEDGMENTSThe authors thank the Ohio Department of

Health/U.S. Environmental Protection Agency fortheir continued support for developing/maintainingthe radon data base for Ohio. The funding is pro-vided to The University of Toledo. The viewsexpressed in this article are those of the authors.

LITERATURE CITED

1. Harrell, J., McKenna, J.P., & Kumar, A. (1993).Geological controls on indoor radon in Ohio,Ohio Department of Natural Resources, Divisionof Geological Survey, Report of InvestigationsNo. 144, 36 p.

2. U.S. National Institutes of Health. National CancerInstitute Fact Sheet. Radon and Cancer: Questions andAnswers. Available at: http://www.cancer.gov/cancertopics/factsheet/Risk/radon. Accessed onSeptember 29, 2009.

3. WHO Handbook on Radon. Available at: http://whqlibdoc.who.int/publications/2009/9789241547673_eng.pdf. Accessed on September 29, 2009.

4. Kumar, A., Heydinger, A.G., & Harrell, J.A.(1990). Development of an indoor radon informa-tion system for Ohio and its application in the

Figure 5. Comparison of prediction errors of kriging and cokriging interpolation techniques. [Color figure canbe viewed in the online issue, which is available at www.interscience.wiley.com.]


study of the geology of radon in Ohio, Ohio airquality development authority, 201 p.

5. Kumar, A., Sud, A., & Heydinger, A. (1998).Application of ORACLE 7.3 database managementsystem for the development of an environmentaldatabase, Environmental Progress, 17, F11–F14.

6. Ojha, S., Thomas, S.J., & Kumar, A. (2001). Expe-rience in integrating geographical informationsystems (GIS) to an indoor radon database, Envi-ronmental Progress, 20, O7–O10.

7. Joshi, A., Manne, G.K., & Kumar, A. (2002). Man-agement of Ohio’s radon data with MS Access/SQL Server 7.0, Environmental Progress, 21, D8–D12.

8. Kumar, A., Tandale, A., Kalapati, R.S., & Ghose,S. (2003). Management of radon mitigation datain the state of Ohio, Environmental Progress, 22,O19–O24.

9. Kumar, A., Harrell, J., & Heydinger, A. (2001).Ohio goes online to combat indoor radon, Envi-ronmental Manager, February, pp. 30–32.

10. Heydinger, A., Kumar, A., & Harrell, J. (1991). AnIndoor radon information system, EnvironmentalSoftware, 6, 194–201.

11. Sud, A. (1998). Update and analysis of a residen-tial radon database for the state of Ohio, MS The-sis, University of Toledo, Toledo, OH.

12. ESRI Website, Ohio Zip Codes Shape Files.Available at: http://www2.census.gov/cgi-bin/shapefiles/state-files?state=39. Accessed onSeptember 15, 2009.

13. Duval, J.S. Aerial radiometric color contour mapsand composite color map of regional surfaceconcentrations of uranium, potassium, and tho-rium in Ohio, U.S. Geological Survey (USGS)Geophysical Investigations Map GP-966, USGSPublications; 1987.

14. Ahmed, S., & De Marsily, G. (1987). Comparisonof geostatistical methods for estimating transmis-sivity using data on transmissivity and specificcapacity, Water Resources Research, 23, 1717–1737.


interpolation of radon concentrations using gis-based kriging and cokriging techniques

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