SUMMARY AND CONCLUSIONS
Contents
1. 8 bit color graphics card allows 256 colors simultaneously 6 16 MB s of RAM 7 35 MB s of free Hard Disk space A3 Acquiring Software The software may be acquired on the internet by using one of the following anonymous ftp or http addresses ftp uncert mines edu http uncert mines edu For anonymous ftp the UNCERT software is stored in the directory pub uncert 172 T 4595 Colorado School of Mines A3 Acquiring Software In this directory releases with executables are available for several UNIX platforms but only the file uncert ver_ tar Z is guaranteed to be current I have limited access to most platforms and all versions may not be current Check the dates on the files The file uncert ver_ tar Z contains the full UNCERT release but no executable files You will have to compile UNCERT yourself if you retrieve this file The UNCERT User s Manual is located in pub uncert manual There are also several useful files in pub misc that may be useful These include public domain and shareware programs available from other locations on the internet These versions may not be the most recent but they may save you time trying to locate them elsewhere These files include f2c a FORTRAN to C preprocessor gcc an ANSI C compiler You need a C compiler to build it gs a Postscript previewer xv a GIF JPEG viewer and gzip a good compression utility There are other file2. Makefile s for each module This is done using the following command select the appropriate command based on your system 174 T 4595 Colorado School of Mines A4 Installation prompt gt set_make ibm IBM RS6000 prompt gt set_make hp HP prompt gt set_make sun Sun OS prompt gt set_make sol Sun Solaris prompt gt set_make sgi Silicon Graphics prompt gt set_make sco SCO prompt gt set_make linux Linux Slackware If your machine type is not listed you will probably need to modify each Makefile in the directories uncert src This will mainly involve defining where the X windows and motif library and include files are located You may also have to define your C and FORTRAN compilers Once the Makefile s are correctly defined type prompt gt build This script will go into each uncert sre directory and try to make each program This may or may not work Several things can go wrong 1 The Makefile s do not have the right libraries specified See if there is a Makefile specific to your machine e g Makefile ibm If there is copy it to Makefile If a correct Makefile does not exist you may have to determine which libraries are missing NOTE on some computers library order is important You do not have an ANSI C compiler or your compiler is named something other than cc If you have compiler other than cc set the variable CC to your compiler name If you don t h
3. Stochastic Imaging and Spatial Distributions Using Hard and Soft Information Master s Thesis Department of Applied Earth Sciences Stanford Stanford University Burden R L and J D Faires 1985 Numerical Analysis Boston Prindle Weber and Schmidt Carle S F and GE Fogg 1996 Transition Probability Based Indicator Geostatistics Mathematical Geology Vol 28 No 4 pp 453 476 Christakos G 1984 On the Problem of Permissible Covariance and Variogram Models Water Resources Research Vol 20 No 2 pp 251 265 Dagdelen K and A K Turner 1996 Importance of Stationarity for Geostatistical Assessment of Environmental Contamination Geostatistics for Environmental and Geotechnical Applications ASTM STP 1283 R M Srivastava S Rouhani M V Cromer and A I Johnson Eds Philadelphia American Society For Testing and Materials Davis B M 1987 Uses and Abuses of Cross Validation in Geostatistics Mathematical Geology Vol 19 No 3 pp 241 248 Deutsch C V and A G Journel 1992 GSLIB Geostatistical Software Library and User s Guide New York Oxford Press Dongarra J J Bunch C Moler and P Stewart 1984 LINPACK Englund E and A Sparks 1988 GEO EAS U S Environmental Protection Agency Environmental Monitoring Systems Laboratory EPA 600 4 88 033 Environmental Science and Engineering 1987 Rocky Mountain Arsenal Water Quantity Quality Survey Final Initial Screening Pro
4. adjusted with anisotropy factors each orthogonal axis may be described and modeled independently This simplifies the modeling process for the modeler because it is not necessary to compromise by selecting one model that acceptably depicts all orientations This advantage is partially offset by the overall computational effort in the kriging process because overall processing time approximately doubles This is a reasonable tradeoff because 1 modeler time is usually more valuable than computer time and 2 most importantly results are more accurate Class conditional indicator simulation versus threshold conditional indicator simulation doesn t appear to reduce model uncertainty nor improve model results yet it is a valuable tool because 1 T 4595 Colorado School of Mines 163 SUMMARY AND CONCLUSIONS Wingle it is a more intuitive approach to defining and modeling indicator semivariograms 2 it facilitates testing of model sensitivity to indicator ordering and 3 it can be argued that although the technique generates more order relation violations these may more accurately represent the true number of problem matrices in the solution In some situations the threshold method fails to identify problems associated with the matrix solution Zonal kriging addresses a common limitation of the geostatistical method at many sites The sample data at many sites do not honor the assumption of second order stationarity that is
5. app defaults N On SGI s you must make this substitution In general if your platform supports this option it is better than XAPPLRESDIR You must also define a help browser If you do not define a browser you will still have on line text help but no graphics for figures We are currently developing the xhelp package but we 176 T 4595 Colorado School of Mines A4 Installation recommend you use netscape Netscape Communications Corporation or Mosaic NCSA These viewers may be downloaded from http home netscape com http www ncsa uiuc edu SDG Software Mosaic NCSAMosaicHome html A version a Mosaic old may be downloaded from our anonymous ftp site if you do not have a web browser The ftp site and file are uncert mines edu pub misc xmosaic 2 5 tar gz At this point netscape has more features but it is a commercial application though they have been letting educational institutions use unlicensed versions To define a browser other than xhelp modify the WWWVIEWER environment variable described above with one of the following commands export WWW VIEWER ustr local netscape export WWW VIEWER usr local Mosaic setenv WWW VIEWER usr local netscape setenv WWW VIEWER usr local Mosaic At this point the UNCERT software should be installed compiled and ready for use In order to set some of the environment variables it is suggested that you logout and then login before you try to run the applications
6. 4 Installation Once you have downloaded the UNCERT software there are several steps you need to follow to install UNCERT 1 Unpack the software 2 compile all the UNCERT modules This step can to skipped if you downloaded a version with executable and 3 set up user accounts A4 1 Unpacking the Software Once you have downloaded the UNCERT package file move it to the directory above where you want UNCERT stored e g usr local To unpack UNCERT type uncompress uncert tar Z tar xvf uncert tar On Linux computers use gzip d uncert tar Z instead of uncompress This will uncompress and un tar UNCERT During the tar process all files will be put in their appropriate locations If you get warning that directories cannot be created you will need to download a script file called mk_uncert_dirs This script also needs to be executed from the directory above where you want UNCERT stored After running this command execute the tar command given above again A4 2 Compiling UNCERT At this point you should read the README file in the uncert directory If you did not download a file with executables or you have trouble with the executables you did download e g cannot find a shared library etc you will have to compile UNCERT Once the files are unpacked change directories to the uncert directory for example prompt gt cd usr local uncert If you are not running on an IBM RS 6000 computer you will need to setup the
7. CHAPTER 7 SUMMARY AND CONCLUSIONS This research presents several new geostatistical methods for modeling subsurface site conditions and a geostatistical ground water modeling and visualization software package The overall goals of developing these methods and tools are to better define site uncertainty reduce site uncertainty or simplify the process of modeling site uncertainty These methods assist hydrogeologists in defining uncertainty in the ground water flow and contaminant transport modeling process so that risks can be more accurately accessed and appropriate remediation methods can be better designed Many of these methods and tools are also applicable to other scientific disciplines 7 1 Summary and Conclusions Jackknifing the semivariogram with small data sets 10 s to 100 s of samples can be useful in describing the uncertainty associated with the definition of the model semivariogram It can be combined with Latin Hypercube Sampling and conditional indicator simulation to model overall site uncertainty but its most useful feature may be facilitating quantitative evaluation of when enough data has been collected at the site to sufficiently describe the site spatial variation Directional semivariograms more accurately model the spatial variation of the sample data Instead of defining a single semivariogram model for the principle axis of site variability and forcing the orthogonal axes of variation to use the same model
8. Inc Isaaks E H and R M Srivastava 1989 An Introduction to Applied Geostatistics New York Oxford University Press Johnson A D 1995 A Geostatistical Evaluation of the Unconfined Aquifer Underlying the Rocky Mountain Arsenal Commerce City Colorado Master s Engineering Report ER 4537 Department of Geology and Geological Engineering Golden Colorado School of Mines Johnson N M and S J Dreiss 1989 Hydrostratigraphic Interpretation Using Indicator Geostatistics Water Resources Research Vol 25 No 12 pp 2501 2510 Journel A G 1983 Nonparametric Estimation of Spatial Distributions Mathematical Geology Vol 15 No 3 pp 445 468 Journel A G and F G Alabert 1988 Focusing on Spatial Connectivity of Extreme Valued Attributes Stochastic Indicator Models of Reservoir Heterogeneities Society of Petroleum Engineers 63rd technical Conference Richardson Texas SPE Paper 18324 pp 621 632 Journel A G and C J Huijbregts 1978 Mining Geostatistics London Academic Press Journel A G and E H Isaaks 1984 Conditional Indicator Simulation Application to a Saskatchewan Uranium Deposit Mathematical Geology Vol 17 No 7 pp 685 718 168 T 4595 Colorado School of Mines Kushnir G and J M Yarus 1992 Modeling Anisotropy in Computer Mapping of Geologic Data Computer Modeling of Geologic Surfaces and Volumes AAPG Computer Applications in Geology 1 Tulsa The American Assoc
9. T 4595 Colorado School of Mines 177 UNCERT AND UNCERT USER S MANUAL Wingle 178 T 4595 Colorado School of Mines APPENDIX B SAMPLE DATA SETS The data sets used in this research are contained on the CD ROM at the back of the dissertation These files are accessible from UNIX systems see mounting instructions in Appendix A and from DOS MS Windows computers with CD ROM drives The files for each chapter are located in the following directories Chapter 2 Jackknifing and Latin Hypercube Sampling data jackknife synthetic test case Chapter 3 Variation of the Semivariogram Models With Direction data direct test synthetic test case data direct rma Rocky Mountain Arsenal test case Chapter 4 Class vs Threshold Indicator Simulation data class test synthetic test case data class survey CSM Survey Field test case Chapter 5 Zonal Kriging data zone test synthetic test case data zone yorkshire Yorkshire England test case data zone survey CSM Survey Field test case Chapter 6 UNCERT uncert full UNCERT distribution uncert html index html on line UNCERT Users s Manual NOTE The filenames follow UNIX naming conventions On DOS and MS Windows 3 11 or older systems filenames may be truncated or modified Descriptions of each data set are contained in README files in each directory T 4595 Colorado School of Mines 179 SAMPLE DATA SETS Wingle 180 T 4595 Colorado School of Mines
10. author or distributor accepts any responsibility to anyone for the consequences of using them or for whether they serve any particular purpose or work at all unless stated so in writing by the authors No author or distributor accepts responsibility for the quality of data generated nor the damage to existing data Everyone is granted permission to copy modify and redistribute the UNCERT package but only under the condition that the copyright notice in the software remain intact The software is provided as is without express or implied warranty A2 Hardware Operating System Requirements The UNCERT software package was written in ANSI C and FORTRAN very little using X windows and motif under the UNIX operating system Currently the software has been tested on IBM RISC 6000 Dec Alpha Data General so I m told HP Linux Silicon Graphics SGI Sun OS Sun Solaris and SCO UNIX workstations with 8 bit color graphics cards The software was written to be easily ported and where possible follows ANSI C standards To use this software you must have 1 UNIX operating system computer 2 ANSI C compiler and a FORTRAN compiler A FORTRAN to C preprocessor is available upon request These must be 32 bit compilers The new 64 bit compilers break the software 3 X windows Release 4 and motif Release 1 1 window manager 4 X windows and motif development packages used at compile time to build X windows motif interfaces 5
11. ave a ANSI C compiler you can get gcc from our ftp site gcc is a shareware C and C compiler It may take some effort to compile Note our posted version is not the most recent version You do not have a FORTRAN compiler or your compiler is named something other then xlf or f77 If you have a compiler other than xlf or f77 set the variable F77 to your compiler If you don t have a FORTRAN compiler you can get f2c from our ftp site It is a shareware FORTRAN to C conversion program You then compile the C Contact me Bill Wingle if you have this problem I m still working on an instruction set The FORTRAN compiler does not recognize the qextname compile option Delete it This is an IBM FORTRAN C compile option In block you cannot find su h segy h libcwp a libpar a or libsu a Remove the DSU compile option This is an option to compile SU Seismic UNIX which most users probably won t have Once you get the Makefile s corrected you can type make in each src directory or you can type build from the uncert directory T 4595 Colorado School of Mines 175 UNCERT AND UNCERT USER S MANUAL Wingle NOTE When you start to port the code you must do a make in the uncert src Xs directory first This builds the library libXs a which most of the programs depend on You can then move to any of the other src directories and start compiling code If you are compiling
12. e C R Eschard A Galli Y Mathieu L Montadert and J L Rudkiewicz 1987 Heterogeneities and Geometry of Sedimentary Bodies in a Fluvio Deltaic Reservoir SPE 16753 SPE Annual Technical Conference and Exhibition Dallas Texas pp 115 124 Richardson A 1993 xvertext mppa3 Ouk ac sussex syma Shafer JM and M D Varljen 1990 Approximation of Confidence Limits on Sample Semivariograms From Single Realizations of Spatially Correlated Random Fields Water Resources Research Vol 26 No 8 pp 1787 1802 Strang G 1988 Linear Algebra and its Applications Fort Worth Saunders College Publishing Van Horn R 1972 Geologic Map of the Morrison Quadrangle Jefferson County Colorado United States Geological Survey 1 24 000 7 5 minute Wessel P and W H F Smith 1991 GMT The Generic Mapping Tools School of Ocean amp Earth Science Technology University of Hawaii Wingle W L and E P Poeter 1992 Evaluation of Uncertainty Associated with Contaminant Migration in Ground Water A Technically Feasible Approach Proceedings of the Fifth NGWA Conference on Solving Ground Water Flow Problems with Models pp 687 695 Zheng C 1990 MT3D A Modular Three Dimensional Transport Model U S Environmental Protection Agency and Papadopulos and Associates Inc Zhu H and A G Journel 1992 Formatting and Integrating Soft Data Stochastic Imaging via the Markov Bayes Algorithm Geostatistics Tr ia 92 Tr
13. e model differences involves the significant differences in methods for resolving the order relation violations in the class and threshold simulations Some of these differences can probably be eliminated but they cannot be completely eliminated due to the nature of the two approaches Finally the procedure for handling gradational and fuzzy transitions between zones is simplistic but functional When a cell is estimated points from neighboring zones may be used in the kriging calculation The equation used to described the spatial variance between the sample point and the cell being estimated is the semivariogram model for the zone in which the cell is located This disregards 1 the relative amount of separation distance in each zone and 2 the possibility that a sharp bounding zone separates the point and the cell These conditions were ignored for computational efficiency but most importantly due to concerns that the kriging matrix could no longer be guaranteed to be positive definite This last issue however was not explored but could be investigated in future work T 4595 Colorado School of Mines 165 SUMMARY AND CONCLUSIONS Wingle 166 T 4595 Colorado School of Mines CHAPTER 8 BIBLIOGRAPHY Ababou R A C Bagtzoglou and E F Wood 1994 On the Condition Number of Covariance matrices in Kriging Estimation and Simulation of Random Fields Mathematical Geology Vol 26 No 1 pp 99 133 Alabert F G 1987
14. gram Report Part I of III Prepared for the Rocky Mountain Arsenal T 4595 Colorado School of Mines 167 BIBLIOGRAPHY Wingle Feldman S I D M Gay M W Maimone and N L Schryer 1990 A Fortran to C Converter Computing Science Technical Report No 149 Bell Communications Research and Carnegie Mellon University Fogg G E 1986 Stochastic Analysis of Aquifer Interconnectedness with a test case in the Wilcox Group East Texas Ph D dissertation University Microfilms International Ann Arbor MI University of Texas at Austin Fogg G E 1989 Stochastic Analysis of Aquifer Interconnectedness Wilcox Group Trawick Area East Texas Bureau of Economic Geology Texas University of Texas at Austin Report of Investigations No 189 Foley J D and A V Dam 1984 Fundamentals of Interactive Computer Graphics Reading MA Addison Wesley Publishing Co GNU 1995 gcc Boston MA Free Software Foundation Inc G mez Hern ndez J J and R M Srivastava 1990 ISIM3D An ANSI C Three Dimensional Multiple Indicator Conditional Simulation Program Computers in Geoscience Vol 16 No 4 pp 395 440 Harding Lawson and Associates 1992 Groundwater Monitoring Program Final Annual Groundwater Monitoring Report for 1991 Vol I of II Prepared for the Rocky Mountain Arsenal Heller D 1991 Motif Programming Manual For OSF Motif Version 1 1 Motif Edition Sebastopol California O Reilly amp Associates
15. ia Kluwer Academic Publishers Quantitative Geology and Geostatistics Vol 1 pp 1 12 170 T 4595 Colorado School of Mines APPENDIX A UNCERTAND UNCERT USER S MANUAL The UNCERT software package and User s Manual Version 1 20 are contained on the CD ROM at the back of the dissertation UNCERT is still a growing software package though and I recommend that if you want to use it you download the most recent version from the ftp site described below The instructions below are designed for someone downloading the software from the internet using anonymous ftp Special instructions for retrieving the software from the CD ROM will be described in italics Al Information and Comments This is a freeware software package so there is little technical support However we are trying to make this package as useful as possible and if you have questions or comments contact Bill Wingle at e mail wwingle mines edu or Department of Geology and Geological Engineering Colorado School of Mines Golden Colorado 80401 303 273 3905 303 273 3859 FAX If you find software bugs or better yet fix software bugs please contact us so that we can improve future releases T 4595 Colorado School of Mines 171 UNCERT AND UNCERT USER S MANUAL Wingle A1 1 Warranty The UNCERT package the program modules within and the user s manual are distributed in the hope that they will be useful but WITHOUT ANY WARRANTY No
16. iation of Petroleum Geologists pp 75 92 McDonald M G and A W Harbaugh 1988 A Modular Three Dimensional Finite Difference Ground Water Flow Model U S Geological Survey Techniques of Water Resources Investigation Book 6 McGill R E 1984 An Introduction to Risk Analysis 2nd Edition Tulsa Oklahoma PennWell Publishing McKay M D and R J Beckman 1979 A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code Technometrics Vol 21 No 2 pp 239 245 McKenna S A and E P Poeter 1994 Simulating Geological Uncertainty with Imprecise Data for Groundwater Flow and Advective Transport Modeling Simulating Geological Uncertainty with Imprecise Data for groundwater Flow and Advective Transport Modeling AAPG Computer Applications in Geology J M Yarus and R L Chambers Eds Tulsa Association of Petroleum Geologists pp 241 248 McKenna S A 1994 Utilization of Soft Data for Uncertainty Reduction in Groundwater Flow and transport Modeling Ph D Dissertation T 4291 Department of Geology and Geological Engineering Golden Colorado School of Mines Myers D E and A G Journel 1990 Variograms and Zonal Aniostropies and Noninvertable Kriging Systems Mathematical Geology Vol 22 No 7 pp 779 785 NCSA 1993 libhtmlw a Champaign Illinois National Center for Supercomputing Applications University of Illinois Olea R A 1974 Optima
17. l Contour Mapping Using Universal Kriging Journal of Geophysical Research Vol 79 No 5 pp 695 702 Orr E D and A R Dutton 1983 An Application of Geostatistics to Determine Regional Ground water Flow in the San Andreas Formation Texas and New Mexico Ground Water Vol 21 No 5 pp 619 624 Posa D 1989 Conditioning of the Stationary Kriging Matrices for Some Well Known Covariance Models Mathematical Geology Vol 21 No 7 pp 755 765 Poeter E P and D R Gaylord 1990 Influence of Aquifer Heterogeneity on Contaminant Transport at the Hanford Site Ground Water Vol 28 No 6 pp 900 909 Press W H S A Teukolsky W T Vettering and B P Flannery 1992 Numerical Recipes in C The Art of Scientific Computing Second Edition Cambridge University Press Punin J R 1994 ASHE A Simple HTML Editor xhtml 1 3 Troy New York Rennselar Polytechnic Institute T 4595 Colorado School of Mines 169 BIBLIOGRAPHY Wingle Rautman C A and A H Treadway 1991 Geologic Uncertainty in a Regulatory Environment An Example From the Potential Yucca Mountain Nuclear Waste Repository Site Environmental Geology Water Sciences Vol 18 No 3 pp 171 184 Ravenne C and H Beucher 1988 Recent Developments of Description of Sedimentary Bodies in a Fluvio Deltaic Reservoir and Their 3D Conditional Simulations Richardson Texas Socitey of Petroleum Engineers 18310 pp 463 476 Ravenn
18. on a non supported system I doubt that you will have to make more than a few changes to get the UNCERT modules compiled There are a couple of important notes though 1 Many of the program directories repeat the same files These are common tool object files that will eventually go into a single library Unfortunately I can t keep all of the files current as I develop UNCERT therefore from directory to directory files may vary slightly and be incompatible This means that if you find a problem in a common file you need to change each file not copy the fixed file to the different directories A4 3 Setting Up User Accounts To run the programs correctly each user will have to have several environment variables defined in their login file ksh gt profile csh gt cshrc etc If you use ksh they are defined as follows export UNCERT usr local uncert export PATH PATH UNCERT bin export UNCERT_TMPDIR tmp export UNCERT_HELP_DIR UNCERT help export XAPPLRESDIR UNCERT app defaults export WWWVIEWER xhelp If you use csh they are defined as follows setenv UNCERT usr local uncert setenv PATH PATH UNCERT bin setenv UNCERT_TMPDIR tmp setenv UNCERT_HELP_DIR UNCERT help setenv XAPPLRESDIR UNCERT app defaults setenv WWW VIEWER xhelp If you use another shell you may have to modify the syntax slightly On some systems XAPPLRESDIR can be replaced with ksh export XUSERFILESEARCHPATH XUSERFILESEARCHPATH Y UNCERT
19. rom these techniques should be tested using flow and transport models at controlled sites to test this premise The questions to ask are 1 do these methods produce more consistent and more accurate results 2 do they help reduce uncertainty in defining contaminant migration pathways and 3 when inverse parameter estimation methods are implemented are the sensitivities for the estimated parameters reduced Two other issues that should be further researched relate specifically to the class and threshold conditional simulation methods It is argued that although the results between the methods are not identical the methods produce substantially the same results This conclusion is based on two observations One is that the differences between the methods are approximately equivalent to the differences using the same method with a different indicator ordering Because ordering is arbitrary theoretically it should not affect model results however there were small local differences for the limited number of simulations calculated 50 to 200 It would be useful to test and confirm that the differences due to indicator ordering or class vs threshold techniques become smaller as the number of simulations is increased possibly to 1000 or more This was beyond the 164 T 4595 Colorado School of Mines 7 2 Recommendations for Future Work scope of this research due to limited computing facilities The second observation related to th
20. s too A typical anonymous ftp session might look like your prompt gt ftp uncert mines edu user name anonymous password your e mail address e g wwingle mines edu ftp gt binary ftp gt cd pub uncert ftp gt get uncert ver_1 20 tar Z ftp gt quit If you want to recover UNCERT from the CD ROM there are several steps you must follow You may need to have root privilege to mount and unmount the CD ROM 1 Mount the CD ROM On IBM RS 6000 workstations you must have root permission Use the following commands prompt gt su prompt gt mkdir cdrom prompt gt mount v cdrfs p r dev cd0 cdrom 2 Install UNCERT The full UNCERT IBM RS6000 release is located in the cdrom uncert directory All files are directly accessible they are not tarred or compressed You can now copy it to your computer For example prompt gt cd usr local prompt gt cp pR cdrom uncert uncert T 4595 Colorado School of Mines 173 UNCERT AND UNCERT USER S MANUAL Wingle You do not have to install UNCERT in usr local This is a common location however 3 Unmount CD ROM This will have to be done as root also prompt gt unmount cdrom If you are using a system other than an IBM RS 6000 the commands for mounting and unmounting the CD ROM may vary Consult your system administrator You will also have to recompile UNCERT Instructions are given below for compiling UNCERT on different UNIX systems A
21. the spatial variation of the data as described by the experimental semivariogram varies across the site The zonal kriging method developed in this research automates some of the methods previously performed manually to address this situation and adds several new tools to cope with transitions between zones Again by allowing the modeler to more accurately describe site conditions this technique generates more accurate site estimates The UNCERT software package incorporates all the methods described above in addition to other statistical and geostatistical methods ground water flow and contaminant transport models and visualization tools This package simplifies the data handling and the use of complex tools thus aiding hydrogeologists in site evaluation and remediation design It is also useful to scientists from other scientific disciplines 7 2 Recommendations for Future Work There are several aspects of this research that could be further developed Some relate to how the methods were tested and evaluated while others relate to limitations of the methods themselves First the methods developed here are tested and evaluated under the premise that if uncertainty is reduced ground water flow and contaminant transport model results will be more accurately match site conditions This is a reasonable supposition but it may not be true Intuitively a model with less uncertainty better describes true site conditions The model results f
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