APPLICATION OF A COMPUTATIONALLY EFFICIENT GEOSTATISTICAL APPROACH TO CHARACTERIZING VARIABLY SPACED WATER-TABLE DATA

Transcription

1 RFr"W/FZD JAN OST control # 1385 John J Q U ~ M Argonne Natonal Laboratory Argonne, L Tel: , Fax: APPLCATON OF A COMPUTATONALLY EFFCENT GEOSTATSTCAL APPROACH TO CHARACTERZNG VARABLY SPACED WATER-TABLE DATA - ABSTRACT Geostatstcal-andyss of hydraulc head data s useful n producng unbased contour plots of head estmates and relatve errors However, at most stes beng characterzed, montorng wells are generally present at dfferent denstes, wth clusters of wells n some areas and few wells elsewhere The problem that arses when krgng data at dfferent denstes s n achevng adequate resoluton of the grd whle mantanng computatonal effcency and workng wthn software lmtatons For the ste consdered, 113 data ponts were avalable over a 14-m2 study area, ncludng 57 montorng wells wthn an area of concern of 15 m' Varogram analyses of the data ndcate a lnear model wth a neglgble nugget effect The geostatstcal package used n the study allows a maxmum grd of 100 by 100 cells Two-dmensonal krgng was performed for the entre study area wth a 500-ft grd spacng, whle the smaller zone was modeled separately wth a spacng n ths mamer, grd cells for the dense area and the sparse area remaned small relatve to the well separaton dstances, and the maxmum dmensons of the program were not exceeded The spatal head results for the detaled zone were then nested nto the regonal output by use of a graphcal, object-orented database that performed the contourng of the geostatstcal output Ths study beneftted from the two-scale approach and from very fne geostatstcal grd spacngs relatve to typcal data separaton dstances The combnng of the sparse, regonal results wth those from the fner-resoluton area of concern yelded contours that honored the actual data at every measurement locaton The method appled n ths study can also be used to generate reproducble, unbased representatons of other types of spatal data NTRODUCTON AND OBJECTVE Spatally correlated envronmental data are abundant at many US Department of Energy (DOE) stes Examples of such data nclude water-level measurements, contamnant dstrbutons, stratgraphc contacts, ranfall records, and ar qualty measurements Geostatstcal methods may be appled on these data to characterze the ste; however, the densty of the data locatons may affect the analyss Data ponts are often dstrbuted as clusters separated by broad areas wth only sparse data The problem wth krgng a data set of ths nature s n achevng an adequate resoluton of the grd Detals n an area of nterest would be smoothed out f the grd were too 1

2 control # 1385 John J Qunn Argonne Natonal Laboratory Argonne, L Tel: , Fax: coarse, whle a grd that were too fne would be computatonally neffcent n areas of sparse data The maxmum grd sze allowed by the software s a related factor that plays a sgnfcant role n grd desgn Ths paper reports on a case study of the characterzaton of an unconfned aqufer's potentometrc surface at a DOE faclty and ts surroundng area 30 mles west of St Lous, Mssour The goal of the study was to produce an unbased, best e&nate contour map of the water-table surface - The local geology conssts of patchy resduum over Burlngton-Keokuk lmestone (Kleeschulte and mes 1994) The upper porton of the lmestone s fractured and hghly weathered Throughout the 14- m2 study area are 113 data ponts pretanng to the weathered lmestone, ncludng 92 shallow montorng wells and 21 sprngs (Fgure 1) Ffty-seven of the montorng wells are, however, confned to an area of nterest of 15 m2 Average head data for the perod were calculated for use n ths characterzaton METHODS Geostatstcs provdes a set of tools specally desgned to handle spatally correlated data (see, for example, saaks and Srvastava 1989) n a geostatstcal characterzaton, the structure of the data s explored by way of a varogrk analyss A grd s desgned for the study area, and varogram parameters are used as nput n a krgng program to determne the mnmum varance, unbased estmate for each grd cell Relatve errors are also determned for the grd cells The geostatstcs software used n ths study was Geo-EAS (Englund and Sparks 1991), a two-dmensonal geostatstcal package produced by the US Envronmental Protecton Agency A lmtaton of Geo-EAS s that the grd has maxmum dmensons of 100 by 100 cells StePlannerm (ConSolve 1993), a graphcal, object-orented database, s used to contour the krgng output StePlannerm contours data by lnear nterpolaton (trangulated rregular network surface), whch works well wth regularly spaced data Because of the dstrbuton of data n ths study, two grds were desgned and separate lugng runs were performed for each One grd covered the entre study area, wth a grd spacng of 500 ft; the other was centered on the DOE ste, wth a grd spacng of 100 ft (Fgure 2) n ths manner, the grd spacngs for the two areas approxmated the typcal data separaton dstances for each zone, and the maxmum grd dmensons of Geo-EAS were not exceeded APPLCATON OF A COMPUTATONALLY EF'J?CENT GEOSTATSTCAL APPROACH TO CHARACTERZNG VARABLY SPACED WATER-TABJX DATA 2

3 control # 1385 JohnJ Qunn Argonne Natonal Laboratory Argonne,L Tel: , Fax: RESULTS ntally, an omndrectonal varogram was analyzed wth Geo-EAS Throughout the separaton dstances of the data locatons, the results ndcated a lnear vaogram model, wth a neglgble nugget effect (Fgure 3) Drectonal varograms were attempted, but too few data were avalable to provde adequate nformaton on possble ansotropy Ordnary JSrgng was performed on the data set twce to generate results for each of the grds The krgng results were dependent on the search parameters specfed For both the coarse and the fne grds, reasonable results were acheved usng a maxmum search radus of 8,000 ft wth a maxmum of 6 data ponts and a mnmum of 3 data ponts n the calculaton of each grd cell value The management of Geo-EAS output was handled by StePlannerm Krged output for the hgh-resoluton area was nested nto the larger grd's output Concdent grd ponts from the coarse grd were deleted The data from the actual 113 data ponts were added n, and StePlannerm contoured the combned data set (Fgure 4) The resultng contours show desred hgh resoluton n the man area of nterest and reasonable contours n outlyng areas Star-step patterns n the contours of Fgure 4 are a functon of the search parameters used, because they dctate whether sprng data ponts were ncluded n the determnaton of 'ndvdual grd ponts CONCLUSONS AND APPLCATONS Use of the nested grd technque and careful manpulaton of krgng output acheved the desred outcome of a reasonably accurate, unbased map of the water-table surface, ncludng detaled resoluton n the man area of nterest Computer run tme was kept to a mnmum, and the approach overcame a lmtaton of the software The methods demonstrated n ths case study can be appled to other DOE stes and can be used to characterze any avalable spatally correlated data The resultng contour maps are unbased and defendable, and show detals where justfed by the data REFERENCES ConSolve, nc, 1993, StePZannerm, verson 12, Lexngton, MA Englund, E, and A Sparks, 1991, Geo-EAS 121 User's Gude, US Envronmental Protecton APPLCATON OF A COMPUTATONALLY EFFCENT GEOSTATSTCAL APPROACH TO CHARACTERZNG VARABLY SPACED WATER-TABLE DATA 3

4 control # 1385 John J Qunn Argonne Natonal Laboratory Argonne,L Tel: , Fax: Agency, EPA 600/8-91/008, Washngton, DC saaks, EC, and Srvastava, RM, 1989, Appled Geostatstcs, Oxford Unversty Press, New York Kleeschulte, MJ; and mes, JL, 1994, Geohydrology, Water Qualtyy>nd Smulaton of GroundWater Flow at the -Weldon Sprng Chemcal Plant and Vcnty, St Charles CountyyMssour, ,US Geologcal Survey Open-Fle Report ACKNOWLEDGMENT Ths work was supported n part by the US Department of Energy, Offce of Envronmental Restoraton, under contract W ENG-38 AUTHORS John J Qunn Tel: , Fax: , E-mal: qunnj@anlgov Lsa A Durham Tel: , Fax: Robert L Johnson Tel: , Fax: Envronmental Assessment Dvson Argonne Natonal Laboratory 9700 S Cass Avenue Argonne, L APPLCATON OF A COMPUTATONALLY EFFlCENT GEOSTATSTCAL APPROACH TO CHARACTERZNG VARABLY SPACED WATER-TABLE DATA 4

5 control # 1385 John J Qunn Argonne Natonal Laboratory Argonne, L Tel: , Fax: FlGURE CAPTONS 1 Ste layout showng locatons of montorng wells and sprngs 2 Combned geostatstcal grds and actual data locatons 3 Model sotropc varogram 4 Krgng results Contour nterval = 10 ft APPLCATON OF A COMPUTATONALLY EFFCENT GEOSTATSTCAL APPROACH TO CHARACTERZNG VARABLY SPACED WATER-TABLE DATA 5

6 8 e e 8, e 8 e

7 ; / *;* / ' /7 - *,l / * / ; /' - 1 f -:- : J, "Y - - ' $ ; * " ' f "; '/- ; --< - ' : : j ; --, ; - -!, /: ' 7/' j - e, -"*', --_ / b ; - g - *3: 'j A 5 * ' - 2 ;* j? ; '% /'* / 1 J * * ', ',-* ---,*; - ; '- ' ', * '? 1 ;=:

8 4000 ' n c v E 2000 ' Lag h, n feet

9 , :, >? ; :!-_ J