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1. F a e ste se de alle en de se men se en me en de de ole de dn EEE EEE EE EE EEE EEE ttttttt tr ttt tt ert tt tt rot tt Ft tte tet tetetteeeeeee T TEEL O 90909 thet rr rr rrr r r rrr 400099 09009000000 6006005000024 ADD AAA AAA is ds de as de 9009000000 L 000900000008204004 the captured locations within the domain 90000900008000D00008LD000000820D00080G0DA0G Sr 009 068004609 4 a 4 or 2 e E 4 el tr t r r 4 404 Pee e i Ge L 09490900904 K t 1 900010 a 0000 0 t i AAA BAG gt ov 0 t ev ee ee 0 Dispersion impacted Transient Tracker particles it is important to keep in mind that this pumping well has a significant impact on the domain boundaries This serves as an important example of how domain boundaries can affect the capture zone additional locations from within the existing domain would be captured if the domain were extended to the point that pumping impacts 8688 7 days with the
2. i OIE COOU are PP FEvilk s Fase i oO mao 200 y 300 200 500 Figure 4 Particles from Transient Tracker and contours from BRICK at T 1000days 13 Figure 5 Particles from Transient Tracker for 2 dispersivity values and zero disper 1000days sivity at T Figure 6 Test case model grid with GHB cells blue and pumping cell red Each grid cell is 100 feet on each side The grid has 100 columns and 50 rows Value Parameter 0 10 2 5 or 0 0 Porosity 50 0 2 50 a a sl 2 g pS ga Bio lS y D AE eo ale DIS aD pels S15 lF Abie Oo SP 1 2 Ayo F s a E D jolo Sl 8 HID un gt A E vo gt pe A E E 20 The following sets of figures depict results from the groundwater simulation and the particle tracking It is worth noting that this test case is not intended to be strictly surface elevations with realistic it was constructed to provide a set of groundwater dramatic changes in the velocity vectors over time the initial steady state groundwater surface due to the general 7 depicts Figure and the well injecting at 250 gpm The particle release locations head boundaries 14 are also indicated Figure 8 shows the groundwater surface for the final stress period Particles were released in the initial steady state stress period which had a duration of 2000 days The second stress period w
3. About this Document This document describes the various functions of the KT3D H20 graphical user interface Attachments and 2 provide the theoretical documentation for the underlying codes KT3D H20 and Transient Tracker This document constitutes a Beta version release that is not complete or fully tested Underlying codes KT3D H20 Version 3 0 is written in VB Net and combines the latest version of linear log kriging program KT3Ddll dll and Transient Tracker First version for kriging with linear log drift called KT3D Ll is developed by modifying popular GSLIB KT3D kriging code then fortran program is compiled as a Dynamic Link Library DLL which is executed using a Visual Basic UI called kt3d_loglin The MapWindow application is a free and extensible geographic information system GIS that can be used to distribute data to others and to develop and distribute custom spatial data analyses MapWindow includes standard GIS data visualization features as well as DBF attribute table editing shapefile editing and grid importing and conversion MapWinGIS ActiveX includes a GIS API for shapefile and grid data with many built in GIS functions Supported Inputs and Outputs The KT3D H20 GUI supports importing data from Microsoft Excel versions 2000 2007 xls xIsx xlsb and xlsm files Microsoft Access versions 2000 2007 mdb and accdb files ESRI Shape Files shp and ASCH It offers several post processing
4. The aquifer hydraulic conductivity in units consistent with the kriging data files Porosity The aquifer porosity Stepsize The length of the particle tracking step If nparticles gt O the number of particles to be placed in an envelop around each ee well listed in the file DWELL DAT and each line segment listed in the file P 2DSINK DAT Note multiple envelopes can be defined see nrads If nparticles lt 0 KT3D H20 expects to find a file PTRACK IN in the working directory that lists particle starting locations xprad The radius of the innermost envelop of particles around each well listed in 2DWELL DAT and each line segment listed in the file DSINK DAT This only applies where nparticles gt 0 Nrads The number of envelopes of particles around each well listed in 2DWELL DAT and each line segment listed in the file 2DSINK DAT This only applies where nparticles gt 0 The radius of each envelop is a multiple of the radius of the inner envelop xprad Nout The frequency with which to report particle locations to the output file PTRACK OUT Locations are only written when the calculation step is a multiple of nout This keeps file sizes smaller Point Sink or Source of Known Strength In order to execute the KT3D H20 linear log approach to kriging for a 2 D water level data set given a KT3D input PAR data set the following steps are required Construct an accessory file 2D
5. 3 3 b p x 1 000 4 500 Lag Distance Meters Figure 12 Residual versus lag distance for paired monitoring points Cape Cod dataset Sermi Variogram Meters Squared Lag Distance Meters 0 Value indicates number of point pairs data support for the plotted bin Figure 13 Calculated semivariogram of residuals from linear log drift model EE EEE ee outline some clear advantages of the linear log approach To accom plish this a comparative analysis of model suitability and accuracy is provided s indicated previously drift model parameters are calcu lated from global estimation of Z u The spatial distribution of Om 500 m residuals is perhaps best appreciated using a horizontal pure nugget semivariogram contouring the drift model and posting the residuals This approach is possible because although kriging is an exact interpolator at the measured data locations point krig ing at estimation locations removed from the data eliminates dis continuities at the measured data locations and provides a map of the least squares drift model surface This realization is presented for the Iinear log model Figure 10 but not the linear drift model which is simply a uniform gradient from north northeast to south southwest For the Cape Cod dataset the residuals do not appear closely related to water level Figure 11 or lag distance Figure 12 nor is any residual trend or global correlation struc
6. Version 3 0 Beta KT3D H2 A Program for Kriging Water Level Data using Hydrologic Drift Terms User manual Version 3 0 Beta E 5 5 Papadopulos amp Associates Inc DESCRIPTION OF THE KT3D H20 PROGRAM SUITE INTRODUCTION orein oreeeciiicieisnre eei E A N E A 1 ABOUT THIS DOCUMENT nireset nne e A O da 2 UNDERLYING COEN 2 SUPPORTED INPUTSAND OUTPUTS dildo 2 DISCEATME Rp AAA 3 TECHNICAL SUPPORT isc 3 INSTALLING AND STARTING KT3D HO Osio icac ali 4 CREATING ANEW PROJECT sais 6 KRIGING TO GENERATE A GRID aiii 7 PREPARING DAA NNN 7 IMPORTING DAA PP 8 SETTING GRD PARA METERS Cadillac eo 9 SETTING KRIGING PARAMETERS cccccccssssssoeseccecccsonsecesseesecccecesadseseesecesccenaseseedseecesenadsssseeeess 10 SELECTING KRIGING TYPES AND DRIP US abia 11 DHT NN 1 2D Horizontal ine sink source Arif escana a NS 12 DONN 13 SETTING VARIOGRAM PARAMETERS ccccsseecseeeecececcsanscsessecsceccccnsassseeecceecesenacsesecsceecesenaascsseecess 14 RUNNING THE RR NNN 16 SINGLE FVENTRRIGNG ss 16 MOLITEV NI ERICIN NG 17 EXPORTING KRIGING RESULTS a dai 18 IMPORTING KRIGING RESULTS cccccccccececececececscscscscseseseceeeescececececetetetessescseseseseseseseseseccececucucecs 18 APPEND NEW EVENTS ccscsccceccccccccccecececececececscsesesesesececececeeececececetetesesscsesesesesesesesesececccecacecs 20 PARTICLE TRACKING posos crea 21 SETTING PARTICLE TRACKING PARAMETERS gun keine 21 SETTING PARTICLE ST
7. Engineering Hydraulics Proceedings of the Fourth Hydraulics Conference lowa Institute of Hydraulic Research June 12 15 1949 New York John Wiley and Sons Roth C 1998 Is lognormal kriging suitable for local estimation Mathematical Geology 30 no 8 999 1009 Skrivan J A and M R Karlinger 1977 Semi vanogram estimation and universal kriging program Program Number K603 Tacoma Washington U S Geological Survey Water Resources Division Volpi G and G Gambolati 1978 On the use of a main trend for the krig ing technique in hydrology Advances in Water Resources 1 345 349 Zheng 1992 Path3D 3 2 A Ground Water Path and Travel Time Simulator Bethesda Maryland S S Papadopulos and Associates Zheng C 1994 Analysis of particle tracking errors associated with spa tial discretization Ground Water 32 no 5 821 828 MJ Tonkin S P Larson GROUND WATER 40 no 2 185 193 193 Attachment 2 Documentation and Verification Package for TransientTracker Documentation and Verification Package for Transient Tracker A Program for Conducting Particle Tracking Contents Contents List of Figures Outline 1 Transient Tracker 1 1 Background 1 2 Approach 1 3 Principal Program Routines e 14 Input 2 2 2 rank aa ra 1 5 Output aaa a a ae 2 Program Verification Data Set 2 1 Verification with Travel Time Derived From Thiem Equation 2 2 Verification with
8. or drawdown in response to horizontal linear features of known extraction injection rate such as interception trenches or infiltration galleries This implementation is based on the Analytic Element Method AEM described by Strack 1989 and further documented and incorporated into the AEM program TWODAN Fitts 2004 The complex potential representing a line sink 1s Q H z 1 Ln Z 1 Z 1 Ln Z 1 5 TT 22 222 6 z2 Zl Where L the length of the line sink source Z a dimensionless complex variable zl z2 are the complex coordinates of the ends of the line z x iyis the point where Z and Q are evaluated Since oL the discharge per unit length is known out the outset then solving for Q is a linear problem that can be included in the linear kriging system of equations This essential information can be distilled and combined with the linear and logarithmic drifts shown in 4 to give H x y A BX CY D Qilogio ri EZ L ri e x y 7 1 Where LG drawdown factor due to effects of the i line sink E the linear regression coefficient for the line sink factors 2 the summation from 1 to m where m the number of line sinks This drift is only compatible with 2 D kriging This drift can be used in combination with the Point Sink or Source of Known Strength and with any of the standard 2D drifts included with KT3D 3 Circular Leaking Pond of Known Strength This drift wa
9. particle more than 1 cell length the step size is recalculated courant xcell size magnitude of velocit SAFETY SINKSTRENGTH using the courant number according to Used to flag low points in the flow field that are not the result of a well or line sink These low points are stagnation areas for particles and cause lengthy runtimes if a particle is allowed to bounce around in these areas The strength is a head difference That is if the head at a node is more than SINKSTRENGTH less than the value of the four surrounding nodes that node is flagged as an internal sink NPARTICLES Number of particles to simulate if NPART is 1 XPSTART Starting x coordinate location for particle YPSTART Starting y coordinate location for particle SPACE If NPART is 0 then a regular grid of particles is simulated SPACE is the spacing between particles for this grid XMIN minimum x coordinate for particle location grid XMAX maximum x coordinate for particle location grid Y MIN minimum y coordinate for particle location grid YMAX maximum y coordinate for particle location grid GRDFILES i The Surfer input files the GRDFILES i listed in Transient Tracker in are grids of the groundwater levels from each timestep of the numerical simulation The grids are associated with the total elapsed simulation time TTIME i at the end of each respective timestep To avoid poten tial issues with location referencing al
10. tab the user can set and view variogram parameters In this version of KT3D H20 only one variogram at a time may be selected This differs from original GSLIB KT3D which accepts unlimited number of variograms For the detailed explanation of variogram parameters please refer to the GSLIB Book For variogram modeling KT3D H20 uses the GSLIB programs gamv and vmodel To model single the variogram click on the Variogram Model button which opens variogram dialog on variogram modeling page In case of multi event projects there are two options to model variogram The first option is to run Variogram model using all data as a one data set and the second options is run Variogram model using each event as a separate data set The Event Selector dialog will appear Select the appropriate events and click OK The UI automatically calculates the E i KTSO_H20 OTT_UnconfinedWithLine k Grid Seth A Krig ype Variogram Part Track MultiEvent Variogram Definition Type of Semivanogram Model it Varlance Contribution c Nudget Constant c0 Mas Horizontal Range hmas Min Horizontal Range hmin Parameters Defining Geometric Anisotropy Azimuth Corrector O a ar Horizontal Anisotropy 10 amp Run Variogram C using all events as one data set Variogram Model Select events For run experimental variogram s model using gamv and plots them on variogram plot as a blue line
11. the assumptions implicit in the linear log drift model such as aquifer homogeneity isotropy and well penetration If hydraulic con ductivity data are available throughout the modeled domain on a fre quency equal to or greater than that of water level data cokriging the water levels with colocated hydraulic conductivity data Deutsch and Journel 1998 might indicate the distribution of error is corre lated to hydraulic conductivity by reducing overall error Parameter Estimation Although a priori knowledge of aquifer properties such as transmissivity T and storage coefficient S is not required or explicitly included within the kriging routine presented knowledge of these properties from long term pumping tests provide valuable means of verifying for example capture zones calculated using the kriged ground water surface By restructuring the linear log drift with the explicit inclusion of T it should be possible to elucidate the opti mum value of T matching the measured data This possibility sug gests a potential for linear log kriging as a parameter estimation pro cedure although this has not been investigated by the authors at this time Conclusions The purpose of this paper is to introduce a simple single step kriging routine that improves on existing methods used with two dimensional water level data The linear log kriging approach was developed as a practical solution to improving the level of inter pretation possible
12. Analytical Solution BRICK 2 3 Verification Using Numerical Solutions References A Surfer ASCII Grid File Format 11 111 O N NR RE e 10 10 12 20 21 List of Figures 1 10 11 12 13 14 Example head surface near a pumping well red circle calculated using a bilinear interpolation and b linear log kriging Example particle tracks using the linear log kriging approach Travel time to reach pumping well calculated using 1 analytical so lution 2 MODPATH and 3 TransientTracker Particles from Transient Tracker and contours from BRICK at T 1000days 2 2 aa Particles from Transient Tracker for 2 dispersivity values and zero dis persivity at T 1000days 0 0 0 0 0 000008 Test case model grid with GHB cells blue and pumping cell red Each grid cell is 100 feet on each side The grid has 100 columns and OO TOWS LL 22 a 2 aa ra Initial groundwater surface rv vr rn kran Final groundwater surface LL rv rv vr rank an Comparison of Transient Tracker and MODPATH results no dispersion Transient Tracker particle paths with longitudinal 2 5 feet and trans verse 0 5 feet dispersion 2 2 0 0 0 ra rar ee Particle locations black at 8688 7 days Dispersion impacted Transient Tracker particles from a point source at 8688 7 days with the advection only track in the packground Capture z
13. Kriging Type and Trend Indicator Kriging type and trend indicator can be selected from the pull down menus in the Krig Type tab For more information on the theory and implementation of different kriging types and trend indicator options refer to the GSLIB User s Guide Drift Selection The standard KT3D program includes nine drifts options In KT3D H20 three additional drifts are added and fully Drift Selection supported the 2D Well function Q2D the 2D Line Sink a n LS2D and 2D Circular Pond P2D These drift terms are M MESA Quadratic Drift in x described below A thirteenth drift 3D partial penetrating well EI SSE drift Q3D is under development and is not yet supported Ml Quadratic Drift in 2 M Cross Quadratic Drift in AY See Attachment for a complete theoretical description of the EKMAN REALT E Cross Quadratic Drift in 27 20 Well Function Q20 M 20 Line Sink LS2D 2D Well function drift M 20 Circular Pond P2D MM 30 part penetr well 30 The approach of kriging ground water levels measured in the vicinity of pumping wells additional drift terms included in KT3D_H20 using a regional linear and point logarithmic drift the latter derived from the Cooper Jacob and or the Thiem equation is fully described by Tonkin and Larson 2002 See Appendix 1 Following 1ts publication the linear log drift was added to the GSLIB KT3D program here called 2D Well Function Q2D This drift is s
14. Larson 2002 and Brochu and Marcotte 2003 describe the incorporation of analytic elements within the kriging method to account for effects due to pumped wells and boundaries By way of example when kriging water level data in the presence of significant groundwater extraction or injection the residuals the difference between the measured data and the fitted drift surface arising from the use of a linear drift typically indicate large local departures from the drift in the vicinity of the wells that correlate with areas of drawdown or mounding in the case of injection wells The use of drift terms in universal kriging based on hydrologic principals such as drawdown in response to pumping can improve the inference that can be drawn from measured water level data This is illustrated in plan Figure 1 and cross section views Figure 2 This is because the component of spatial correlation in the water levels that results from the influence of the boundary is explicitly included in the drift Hence residuals are typically smaller when an appropriate drift is used This ensures that a smaller proportion of the spatial covariance or correlation must be explained through the use of a variogram the proper estimation of which might require much more data than are available The incorporation of drift terms based on hydrologic principles is described in Tonkin and Larson 2002 and Brochu and Marcotte 2003 Linear Drift Model Linear Log D
15. PLOT Version 3 A particle tracking post processing package for MODFLOW the U S Geolog ical Survey finite difference ground water flow model Open File Report 94 464 U S G S Press W B Flannery S Teukolsky and W Vetterling 1992 Numerical Recipes in Fortran 77 The Art of Scientific Computing 2 ed 992 pp Cambridge University Press Cambridge Prickett T T Naymik and C Longquist 1981 A Random Walk Solute Transport Model for Selected Groundwater Quality Evaluations Illinois State Water Survey Urbana rep 1 11 ed Skrivan J and M Karlinger 1977 Semi variogram estimation and universal kriging program program number K603 U S Geological Survey Water Resources Division Tacoma Washington Tonkin M and S Larson 2002 Kriging water levels with a regional linear and point logarithmic drift Ground Water 40 2 185 193 Zheng C 1992 PATH3D A Groundwater Path and Travel Time Simulator S S Papadopulos and Associates Inc 3 ed Zheng C and G Bennett 2002 Applied Contaminant Transport Modeling second ed John Wiley and Sons Inc New York NY 21 A Surfer ASCII Grid File Format The entries in the header and the data can be space comma or tab delimited DSAA header D must be first character on first line ncol nrow number of columns number of rows xmin xmax minimum x coordinate of grid maximum x coordinate of grid ymin ymax minimum y coordinate of grid maximum y co
16. Verification with Travel Time Derived From Thiem Equa tion The explicit solution of the Thiem equation for particle travel time to a well Neville 2007 was used to estimate particle travel time from a variety of distances to a fully penetrating well in a confined homogeneous system Results were also generated us ing MODFLOW and MODPATH A Surfer grid file was made from the MODFLOW calculated potentiometric surface Particle tracking using Transient Iracker and the Surfer grid file was performed to create a third set of results All three sets of results are included in Figure 3 The results shown in Figure 3 demonstrate excellent agreement between the three methods The parameters used for this simulation are listed in the table below Hydraulic a m day 0 864 Aquifer Thickness Well radius m 1000 Pumping rate m3 day MODFLOW Square grid cell size m MODFLOW Grid dimensions E x a 2 2 Verification with Analytical Solution BRICK Transient Tracker particularly the dispersion process component was verified by com paring the results with an analytical solution of a simple transport scenario The an alytical code BRICK Neville 2006 was used to generate contours of concentration at 1000 days after an initial released from a square source zone measuring 5 feet on each side The following inputs were specified for BRICK Porosity F Velocity L T 0 25 Longitudinal Dispersivity L 10 0 Lateral Transv
17. are described Inputs required to implement each boundary drift term are described in the section KT3D H20 Program Inputs 1 Point Sink or Source of Known Strength This drift was added to account for mounding or drawdown in response to injection or extraction at a known rate at one or more wells For a single well the Thiem equation states that for consistent units 2 30 R o 3 pe TT a 3 3 Where r radial distance from the pumped well R radius of influence Sr drawdown due to pumping Q pumping rate T aquifer transmissivity Examination of 3 indicates that pumping at a single well produces a logarithmic pattern of drawdown centered on the pumping well Under certain assumptions superposition can be used to sum the effect of multiple extracting or injecting wells This essential information can be distilled and combined with the linear drift shown in 2 to give H x y A BX CY D2 Qilogio ri e x y 4 Where Qilog1o ri drawdown factor due to pumping at the i well D the linear regression coefficient for the drawdown factors n ps the summation from to n where n the number of pumped wells 1 A full derivation of 4 is given in Tonkin and Larson 2002 This drift term can be used in combination with any of the standard two dimensional drifts included with KT3D 2 Horizontal Line Sink or Source of Known Strength This drift was added to account for mounding
18. coordinate The resultant ground water elevation is then h 100 0 001X 0 00LY s 9 where s is the net drawdown mounding at i j in response to pumping Ground water elevations were calculated at 40 imaginary monitoring wells within the domain the locations of which were generated from a two variable uniform random field Drawdown and mounding at each point was calculated using Equation 4 Ground water elevation contours were then constructed by gridding the water levels at these 40 points using the linear and linear log drift mod els Because this imaginary dataset is constructed using the theory explicit in the linear log drift model the linear log kriging routine can be expected to exactly represent the structure present Perhaps the most notable difference is that in the linear drift figure the cen ters of highest drawdown and mounding are removed from the extraction and injection wells respectively Figure 8 This effect would be overcome by measuring water levels in the extraction and injection wells However water levels measured in pumping wells are often unrepresentative of levels in the formation adjacent to the well screen due to well losses This circumstance is particularly evi dent in injection wells that have suffered severe fouling and resul tant loss of efficiency 190 M J Tonkin S P Larson GROUND WATER 40 no 2 185 193 Residual Meters Water Level Meters Figure 11 Residual vers
19. drift b linear drift and c linear log drift mm om 200 m 400 m Figure 7 Example of well arrangement and uniform regional gradient removed at these sinks This situation contradicts Operations and maintenance information indicating that these wells were Operating at their design extraction rates In this example the linear log drift generated a gridded dataset that is more representative of the physical conditions expected in the modeled domain and suitable for particle tracking analysis for preliminary estimates of well capture zones This improvement arises largely from the closer approximation of conserved flow con ditions calculated with the linear log drift and provides a defensi ble basis for using the gridded surface to conduct particle tracking analyses Deviations from conserved flow are largely determined by the magnitude and distribution of residuals from the linear log drift model and violations of assumptions underlying the Theis approximation Analysis of the effects of grid discretization on estimation of well capture zones using the linear log method is not entered into here These can be expected to be comparable to those effects arising in two dimensional finite difference ground water model ing as described by Zheng 1994 In general ideal grid dis Figure 8 Ground water elevation contours calculated from linear and linear log drift models M J Tonkin S P Larson GROUND WATER
20. from measured ground water level data Providing that violations of the assumptions accompanying the Theis approx imation are limited application of the method described herein pro vides a gridded ground water surface suitable for tracking particles to estimate well capture zones The surface created comes closer to conserving flow than when a linear drift is used Preliminary esti mates of well capture can be made within moments of water level measurement For an ideal homogeneous isotropic aquifer with fully penetrating wells the gridded surface may be considered as a cal ibrated two dimensional model of the potentiometric surface In cases where these limiting assumptions are fairly well adhered to consideration of the effort and accuracy of numerical modeling ver sus the method described might indicate the latter to be a more cost beneficial approach to estimating plume capture Additional poten tial exists for a single step estimation of aquifer transmissivity Acknowledgments The authors wish to thank the Air Force Center for Environmental Excellence AFCEE Massachusetts Military Reservation Cape Cod for releasing the dataset used in this study and to Michael Karlinger for advice and insights into kriging theory The authors wish to thank the reviewers for their insightful com ments In particular those of Greg McNulty prompted the jack knifing analysis that solidified the manuscript Further Information Copies
21. kriging over other interpolation methods is that in the absence of measurement error or replicates co located data it is an exact interpolator Chiles and Delfiner 1999 provide a detailed summary of kriging Two popular forms of kriging employed for interpolating real valued data are 1 simple kriging and 2 ordinary kriging In simple kriging the mean of the data m is assumed to be constant everywhere and its value known a priori In ordinary kriging the mean is assumed to be unknown a priori and is estimated using either all or some local moving neighborhood of the measured data The methods described in this discussion are based upon ordinary kriging In the most common implementation of ordinary kriging the mean is assumed to be constant and equivalent to the mean of the data that is m m x However ordinary kriging can support a spatially varying mean which is commonly described as a smoothly varying mean or drift When a spatially varying mean is incorporated the kriging estimate can be illustrated as the sum of two components the mean and a zero mean residual H x mx x 1 Where H x the kriging estimate m x the smoothly varying trend or drift e x the zero mean random residual from the drift This approach is commonly referred to as Universal Kriging UK This trend is usually a simple function of the spatial coordinates such as a linear or quadratic function of the data X and Y coordin
22. locations are saved in memory To add more particles simply draw another polyline 2 To draw a polygon From the Custom Particles toolbar select the shape of polygon irregular n sided regular or rectangular Left click to start the polygon and right click to end it To draw a square select the rectangle tool and hold down the Ctrl key while drawing the rectangle Particles may be generated inside the polygon one of two ways either enter the number of particles next to of Particles which will generate the set number of particles at random locations inside the polygon or eie check Use Grid Nodes to generate Use Grid Nodes particles at all kriging grid nodes inside the pg polygon a e EA DE Locations 23 To use existing polygon shape file In the Custom Particles dialog select the shapefile import tab from the dialog toolbar Select the polygon shape file from the legend then select desired shape Enter number of particles as explained in section 2 above and click Add Particles To generate a point shapefile from generated particle locations click Create Shape File After generating particles click OK The UI will populate a particle worksheet with particle coordinates d Custom Regular Grid Select Custom Regular Grid cc 99 Cells Size from the pull down menu next to Starting Loc Options Enter X and Y coordinates and cell size Default values are grid extents used in th
23. sink source The correspondence that successfully led to the inclusion of this drift term helped greatly with our understanding of the Analytic Element Method Technical Support Limited technical support can be obtained by writing to matt sspa com Frequently Asked Questions How can I make a map of my best fit drift trend surface assuming that the errors in the measurement data are uncorrelated just to see a map of it This is analogous to performing a least squares fit of the function Z A BX CY D Q E L FP e Where A B C D E and F are drift coefficients X Y are Cartesian coordinates Q is the 2 D well drift component summation L is the known strength line sink source drift component summation P is the known strength circular elements drift component summation The error term i e residual is not included the gridded surface will not be an exact interpolator but will be the best fit of the trend Theoretically fitting of this surface is achieved using a horizontal pure nugget variogram With the code provided this 1s achieved by setting the variogram parameters a_hmin a_hmax a_vert to 0 1 0 1 0 1 and setting the trend variable to 1 estimate trend Should I include water levels measured in extraction wells in the observed water level data set Since the linear log drift accounts for the effects of extraction or injection water levels measured in extraction wells should in ge
24. the drift model for krig ing water level data has been previously proposed but to our knowledge not presented Volpi and Gambolati 1978 The approach presented here arose without knowledge of this prior study and 1t is hoped complements and extends the discussion presented therein with some examples Drift Model Kriging using a drift or trend model termed universal krig ing is typically performed where a smoothly varying trend is present in the data The drift component is usually modeled as a function of the data coordinates whose unknown parameters are fit ted from the data Deutsch and Journel 1998 The underlying model is then the sum of the drift component plus the residuals Z u m u R u 1 where Z u value of random or regionalized variable m u drift trend R u residual component u Cartesian coordinate location x y for two dimensional kriging The residual component is typically modeled as a zero mean sta tionary random function RF Deutsch and Journel 1998 A linear drift is defined as the least squares fit of the planar sur face described by Linear drift A BX CY 2 where X is x or easterly coordinate dimension of length L Y is y or northerly coordinate L and A B and C are fitted param eters of the drift model calculated from the data The kriging algorithm identifies the least squares fit of the dnft model to the data assuming that residuals R u are uncorrela
25. trenches rivers and ponds when kriging groundwater level data Use of the KT3D H20 programs should always be accompanied by review of the documentation for KT3D provided in the GSLIB book Deutsch and Journel 1992 Background Though kriging is widely used for constructing gridded datasets suitable for contouring when kriging water levels in the vicinity of pumping wells rivers and trenches large departures from the underlying trend are evident that correlate with areas of drawdown or mounding and that render the maps aesthetically displeasing and illustrate weaknesses in the interpretation of the data The methods incorporated in the KT3D H20 programs mitigate some of these weaknesses by including information in the kriging process to account for these features This information is included through the description of an assumed underlying trend in the data In this document the term drift is used synonymously with the term trend to describe a pattern that has a deterministic source or can be approximated by deterministic means Since the method is based on automated gridding it can be more consistent between data sets and between analysts than methods based on hand contouring Since the method is based on Universal Kriging a brief overview of Universal Kriging is provided first Universal Kriging Kriging is employed in the hydrologic disciplines for interpolating measured data to regular grids suitable for contouring One advantage of
26. wish to export 28 References Deutsch C and Journel A 1992 GSLIB Geostatistical Software Library and User s Guide Oxford University Press 340 pp Tonkin Matthew J and Larson Steven P 2002 Kriging Water Levels with a Regional linear and Point logarithmic Drift Ground Water March April 2002 MAP WINDOW Desktop User Guide http www mapwindow org wik1i index php Map Window Desktop 29 Appendix A KT3D_H20 Input Formats KT3D H20 supports importing data from Microsoft Excel versions 2000 2007 xls xlsx xlsb and xlsm files Microsoft Access versions 2000 2007 mdb and accdb files ESRI Shape Files shp and ASCII txt or dat files with values separated by space comma or tab Water Level data KT3D H2O required following set of variables in input data First line IS assumed to be header line for example X Y WL Well DDate then for each measurement line with XC YC G Value 1 OID 1 Event 1 Variables 1 Header Line 2 XC YC 1 Value 1 OIDG Event 1 Where this line is repeated n measurements times The table below provides explanation of the variables used in KT3D H20 input data XC i X coordinate of the object 1 YCGi Y coordinate of the object 1 Value i Kriging variable 1 OID i Name of the object 1 Event i Date of the event Required for Multi Event projects 30 By default KT3D H20 assigns the first column in your input data as X coo
27. 40 no 2 185 193 189 Meters msl Lineer Drift Profle Regional Gradient Known O Linear log Drift Profile Figure 9 Profile of regional hydraulic gradients calculated from linear and linear log drift models cretization 1s proportional to the magnitude of the source s and sink s simulated and in this respect is case specific Regional Hydraulic Gradient Accurate estimates of the background or regional gradient are particularly important where compliance objectives for pump and treat systems include restrictions on gradient changes outside the impacted area A hnear drift can be considered as a least squares fit of a planar surface to the ground water levels To reduce the over all error throughout the gridded domain the kriging routine may cal culate an unrealistic underlying trend that is biased by the location of monitoring wells near pumping wells By way of example Figure 7 shows an artificially generated uniform background poten tiometric surface The area of interest is 1000 x 1000 m Superimposed on this surface are 1 a well extracting 3 15 x 10 m sec in the northeast upgradient quadrant and 2 a well inject ing 3 15 X 102 m sec in the southwest downgradient quadrant The underlying uniform hydraulic gradient from northeast to southwest was generated with the equation h 100 0 001X 0 001Y 8 where his the elevation at location i j X is the x coordinate and Y is the y
28. 74772E 03 4 13733E 03 P0002 3 74785E 03 4 13572E 03 P0003 3 74797E 03 4 13411E 03 P0004 3 74809E 03 4 13250E 03 P0005 or OW OO OO DO 15 Particle Release L oah as 1065 gar 1055 a p 1045 AE 1035 A 1025 102 1015 1005 qr 995 985 ST 365 wr k E EN 7 oe a P Figure 7 Initial groundwater surface Figure 8 Final groundwater surface 16 Figure 9 Comparison of Transient Tracker and MODPATH results no dispersion The gray particles in Figure 9 are the MODPATH particle tracking results The black particles are the Transient Tracker results The two methods provide nearly identical paths Path3D results are not shown since they were indistinguishable from these results This figure provides a demonstration that Transient Iracker is capable of representing advective particle transport in homogeneous aquifers Particle tracks in Figure 10 demonstrate the longitudinal 2 5 feet and transverse 0 5 feet dispersivity impacts using the same line source and conditions as in Figure 9 Dispersion in this figure is simulated using the Prickett et al 1981 random walk algorithm In Figure 11 the same particle tracks are shown in the background and in the foreground are particle locations at 8688 7 days after the start of the simulation This cloud of particles illustrates the considerable differences in travel time experienced by the various particles as a result of small differences in
29. ARTING OT 22 kunning parlicle SEE 25 HYDRAULIC CAPTURE ZONE ANALYSIS sscsisossccscccssscssecsssessocssvesssccnsseoseosesessocsssessessssesse 27 EXPORTING HYDRAULIC CAPTURE ZONE ANALYSIS RESULTS cccccccceccccceeeeeeeeesessseseeeeeeeeeeeeees 28 REPERENCES cidad 29 APPENDIX A_KT3D_H2O0 INPUT FORMATS eesosssssseccccccccssssesececocosssssececocssssssseeessossoe 30 APPENDIX B BINARY FILE FORMATS siscsicsssccissccecessssssocasecsvendesvivescsseestadasesvecosssssbosesweveee 33 APPENDIX C ARCINFO ASCII GRID FILES FORMATS eessseessssecccssccccssecccsseccecssececoseeooo 35 Attachment 1 KT3D_H20 v3 0 A Program for Kriging Water Level Data using Hydrologic Drift Terms Theoretical Documentation Attachment 2 Documentation and Verification Package for TransientTracker Introduction KT3D H20 Version 3 0 is a graphical user interface GUI that combines various programs to generate gridded maps of water level elevations particle tracks and capture zones These tools combine geosatistical and hydrological sciences to allow the user to generate map based hydrogeologic analyses outputs without having to revert to numerical or analytical models KT3D H20 is developed as a plug in application under the open source GIS foundation MapWindow It allows the user to generate gridded maps of water level elevations that include the following elements that have important influence on the shape of the mapped surface and are usually ignored by o
30. INEFILES i TTIME i This line is repeated NGRD times IBACK NPTP COND POR STEP NPART XPRAD NRADS ES NOUT MAXTIME 9 ALPL ALPT PORZ ROERR TINY SAFETY EPS VSMALL COURANT SINK STRENGTH Items 11 or 12 are entered depending on the value of the NPART flag nparticles NPARTICLES XPSTARTG YPSTART j This line is repeated NPARTICLES space SPACE 12b xmn XMIN 12c xmx XMAX 12d ymn YMIN ymx YMAX The following provides an explanation of the variables required in Transient Tracker in and some of the options regarding the possible values NGRD Specifies the number of grid files to be used by the program Typically one grid will reflect a steady state flow field and multiple grids reflect changing flow conditions with changing stresses NCOL Number of columns in the Surfer grid files NROW Number of rows in the Surfer grid files XMN Minimum value of the x coordinate nodes the x coordinate of MIN the node in the Ist row Ist column YMN Minimum value of the y coordinate nodes the y coordinate of IN the node in the 1st row 1st column WELFILES Well file names LINEFILE Names of each line source file TTIME Termination time time at which the associated grid file ceases IBACK Flag for selecting forward or backward tracking 1 for forward AE tracking 1 for backward tracking Total number of particles transport steps to simulate COND Hydraulic conductivity of the porous med
31. WELL DAT that contains information required to define the well location s and extraction injection rate s The format of this file is shown below Change the tenth drift term in the PAR file from 0 to I Use the modified KT3D_H20 program Format of file 2DWELL DAT n Number of wells X 1 YG Q QTA X Y coordinates rate type for first well X n Y n Qn QT n X Y coordinates rate type for last well The purpose of QTYPE is to indicate if the well is considered a Recovery Well QTY PE R for which it is necessary to map and illustrate particle capture or a non Recovery Well QTYPE NR at which particles may be recovered but for which it is not necessary to map and illustrate particle capture Horizontal Line Sink or Source of Known Strength In order to execute the KT3D H20 horizontal line sink or source of known strength given a KT3D input PAR data set the following steps are required Construct an accessory file 2DSINK DAT that contains information required to define the line sink sources including the segment location s and extracion injection rate s The format of this file is shown below Change the eleventh drift term in the PAR file from 0 to I Use the modified KT3D_H20 program Note that the rate or strength of the line segment is specified in terms of rate per unit length For example a 10 foot segment with a total extraction of 10 gpm h
32. Z data to krig Microsoft Excel xIs xIsx xisb Z value at each location variable to Z value at each location variable to eg water or xIsm Microsoft Access krig e g water elevations krig e g water elevations elevation mdb or accdb ESRI measurements shapefile shp ASCII txt or at wells dat Location Name e g well ID Location Name e g well ID Event date Optional Drift Terms for Water Level Kriging Supported input file type Drift Type Required components X Y coordinate at the center of each pond Microsoft Excel xls xlsx xIsb or xlsm Microsoft Access Pond drift mdb or accdb ESRI shapefile shp ASCII txt or dat X Y coordinates which define each line minuimum two points Microsoft Excel xIs xIsx xIsb or xIsm Microsoft Access Line Drift mdb or accdb ESRI shapefile shp ASCII txt or Sink strength dat xparfile single event kriging xpars mult event kriging X Y coordinate of each injection or X Y coordinate of each injection or extraction location extraction location Injection or extration rate at each Injection or extration rate at each Microsoft Excel xIs xIsx xIsb oganon o atian or xIsm Microsoft Access Injection or extraction location name Injection or extraction location name Well Drift mdb or accdb ESRI e g Well ID e g Well ID snapene SA 18 SEO Drift term flag for each location Drift term flag for each location Ind
33. a regular grid of 200 x 200 points spaced on a 7 X7 m grid assuming no drift a lin ear drift and a linear log drift In each case a linear semivariogram M J Tonkin S P Larson GROUND WATER 40 no 2 185 193 187 Om 500m 1000m Figure 4 Comparison of ground water contours a no drift b linear drift and c linear log drift Modeled Meters Measured Q Linear Log Drift 4 Linear Drift Measured Meters Figure 5 Calculated versus measured water level for linear and jinear log drifts was used Visual comparison of the ground water contours on the three resulting maps Figure 4 indicates 1 In areas of high data control closely spaced monitoring wells and low stress far from pumping contours of the no dnft the linear dnift and linear log maps are similar 2 In areas of high data control closely spaced monitoring wells and high stress close to pumping the contours of the no drift and hnear drift maps are similar however contours of the linear log map exhibit the more defined structure of the under lying drift model 3 In areas of low data control contours of the no drift linear drift and linear log maps differ markedly In particular contours of the no drift map converge in the north of the domain where a single data point is present resulting in an unrealistic map of the ground water surface As the distance from measurement points increases the under lying d
34. above copyright notice remain intact The current release constitutes a Beta version that has not been fully tested Technical Support Technical support regarding use of the graphical user interface can be obtained by writing to karanovicm sspa com Installing and starting KT3D H20 Installation Requirements It is assumed that KT3D H20 users already have some basic understanding of kriging techniques and GIS concepts It is assumed that user already has installed the latest version of MapWindow which can be downloaded at The latest version of the MapWindow book can be purchased or downloaded free from http www lulu com Also the Ist edition of book is included in KT3D installation file To install KT3D_H20 using the setup file follow these three steps l Download the installation program KT3D H20 Setup exe from www sspa com 2 Run the installation program following instructions on the screen The destination folder must be the MapWindow root folder usually C ProgramFiles MapWindow 3 The setup program installs all necessary Dynamic Link Library files dll s user s manuals and sample files into appropriate MapWindow folders After installing KT3D H20 open MapWindow Click on Plug Ins from the Map Window toolbar and select KT3D H20 This will add KT3D H20 to the MapWindow toolbar If KT3D_H20 is not listed under Plug Ins make sure that the file SSPA To
35. advection only track in the packground captured While Figure 13 demonstrates were not significant at the boundaries Figure 12 from which a particle that Gray crosses indicate particles black circles Figure 13 Capture zone indicating the locations released will be captured by the recovery well leave through a domain boundary 19 Technical Support Limited technical support can be obtained by writing to mattQsspa com Disclaimer This software is provided AS IS without warranty of any kind including without limitation the warranties of merchantability fitness for a particular purpose and non infringement The entire risk and responsibility as to the quality and performance of the Software is borne by the user The author s disclaim all other warranties 20 References McDonald M G and A W Harbaugh 1988 A Modular Three Dimensional Finite Difference ground water flow model USGS Techniques of Water Resources Inves tigations vol 06 A1 United States Geological Survey USGS Reston Virginia Neville C 2006 Analytical Solutions for Solute Transport with One Dimensional Flow Brick Sources in an Infinite Aquifer S S Papadopulos and Associates Inc Bethesda MD Neville C 2007 Groundwater Travel Time to a Single Extraction Well Screening Level Analytical Solutions S S Papadopulos and Associates Inc Bethesda MD Pollock D W 1994 User s guide for MODPATH MODPATH
36. an be a subjective exercise and comparison of kriging standard deviations and or Lagrange multipliers includes this 192 MJ Tonkin S P Larson GROUND WATER 40 no 2 185 193 Squared Meters o amp 40 60 80 100 Percentile O Linear log Modei Percentiles OLinear Model Percentiles Figure 16 Percentile plot of squared residuals from the jackknifing analysis O Linear tog error gt 2 0 times linear error Linear tog error lt 0 5 times linear error Extraction Well Figure 17 Map of relative error from the jackknifing analysis subjectivity For this reason the authors have attempted in the fol lowing to present a concise comparative analysis of model errors arising from the linear log and linear drifts alone i e errors related to modeling the m u term and avoid a discussion of errors related to semivariogram modeling Numerous methods of varying complexity are available to assess or compare the correctness of model structure Principal among these in geostatistics 1s jackknifing or single point cross validation In this method each data point is in turn suppressed removed from the dataset and estimated using the kriging model based on the remaining data The differences between the measured value and estimated values can be squared and summed and this value used to indicate the accuracy of the model This approach has ee te EE ES NE a ae ak e rr been used to compare the linear log and l
37. arbaugh 1988 This particle tracking approach can be used to indicate the relative timing of the arrival of contaminants at potential re ceptors and or points of calculation POCs This particle tracking approach is based upon that implemented in the MODFLOW compatible particle tracking code Path3D Zheng 1992 which has been demonstrated to provide very similar results to the USGS particle tracking program MODPATH Pollock 1994 The RK4 scheme that is being employed also incorporates Random Walk RW approaches for representing the spreading of contaminants through time due to dispersive effects Prickett et al 1981 Zheng and Bennett 2002 Either of the approaches Prickett et al 1981 or Zheng and Bennett 2002 are available selected by a flag in the input file see input instructions below It is noted that these methods are not mass conservative that is while they can consider the affects of advection retardation and dispersion they do not consider or conserve the mass of contaminants that are in the groundwater The method employed by Transient Tracker offers a rapid visual means of assessing the potential uncertainties in solute transport directions which will be critical for efficient evaluation of large numbers of potential scenarios and assessing impacts of parameter uncertainty TransientTracker uses the linear log kriging pumping well drift approach of Tonkin and Larson 2002 to calculate a more reasona
38. as a rate strength of 1 0 gpm ft The format of the file 2DSINK DAT depends on the method being used to define the line sinks If line sinks are isolated in space then NLIN must be gt 0 and the start and end of each line segment must be specified In this case there will be NLIN x 2 entries in the file If line sinks are connected at their ends then the user can opt to only list the points that define the total line In this case the number of actual line segments will be NLIN x 2 1 and the start of each subsequent segment is identified by KT3D H20 as the end of the previous segment Note that presently this option can only be used if every segment is of equal strength per unit length this 1s not a limitation of the method Format of file 2DSINK DAT if NLIN gt 0 nlin Number of line segments Ixs i lys l1G lv X start Y start flag rate for first segment IxeQ lye iG IvG X end Y end flag rate for first segment Ixs nlin lys nlin li nlin lv nlin X start Y start flag rate for last segment Ixe nlin lye nlin li nlin lv nlin X end Y end flag rate for last segment Format of file 2DSINK DAT if NLIN lt O nlin number of line segments nlin x 2 I Iixs y lysG lindG Ival X start Y start flag rate for first segment Ixe nlin lye nlin li nlin Ivmlin X end Y end flag rate for last segment Example Data Sets Note examples to be converted to be used in KT3D H20 GUI V
39. ates However the kriging formulism is not limited to this form of drift and is generally only limited to drift functions that can be fit through the solution of the linear system of kriging equations For discussion on the use of trends in kriging refer to Volpi and Gambolatti 1978 Kriging with a linear trend model or drift is available through popular programs such as Surfer and TecPlot A linear drift is suitable in situations where unidirectional regional groundwater flow exists a condition often encountered The UK estimator for gridding water level data using this approach can be illustrated as H x y A BX CY e x y 2 Where H x y the estimated elevation at location X Y X the easting or X ordinate Y the northing or Y ordinate A B C coefficients for the plane fitting the groundwater heads e x y the residual from the drift The linear drift may not be suitable in areas a where singularities occur within the data field such as created by pumping wells b where lateral hydrologic boundaries such as the lateral termination of aquifer materials are present c where there is a significant vertical component of flow and or d where there are substantial changes in aquifer properties or preferential pathways If these effects can be represented in the trend using appropriate functions with linear coefficients these difficulties can be resolved and kriging can produce suitable maps Tonkin and
40. ble representation of the veloc ity field near pumping wells compared with a bilinear interpolation scheme Figure 1 In addition the velocity field converges on the well Figure 2 which can be expected to produce more reasonable capture zones 1 3 Principal Program Routines The principal routines in the code are listed below along with brief descriptions rkasc and rk4 These two routines perform a 4th Runge Kutta solution to de termine the future particle location The routine rkasc monitors trunca tion error and performs step size adjustment while rk4 handles the mul tiple calls to the velocity interpolation routine accumulates the multiple estimates and weights them to provide the updated particle location vpoint This routine performs simple linear interpolation of velocity between grid nodes The routine also checks for strong sinks or strong sinks in adjacent cells When evaluating velocity in weak sink cells the routine invokes an analytical solution to determine the velocity vector within a cell krig Kriging algorithm from Skrivan and Karlinger 1977 used to calculate velocities for particles near wells according to the method described by Tonkin and Larson 2002 pzdispersion Particle dispersion is implemented through this routine using either Prickett et al 1981 or Zheng and Bennett 2002 depending on the flag setting in the input file This routine is not invoked if all dispersivities ar
41. ccccncnnnnnnoncnncnnnnonononononncnnnnnnos 10 3 CIRCULAR LEAKING POND OF KNOWN STRENGTH osorrnnnrvvnvrrnnnnnnnnnrnvnnvrnnnnnnnnessnnnnrvnnnnnnnsnsnnenn 11 KTD H2O PROGRAM INPUTS sansene 13 NEW PAR TE VRIS 13 POINT SINK OR SOURCE OF KNOWN STRENGTH avse 14 HORIZONTAL LINE SINK OR SOURCE OF KNOWN STRENGTH rrrnrnnnvnnvvvnnnnnnnnnrnnnnvvnnnnnnnsrsnnnnnrnnnnn 15 EXAMPLEDATA SETS gs 17 NOTE EXAMPLES TO BE CONVERTED TO BE USED IN KT3D_H20 GUI VERSION GT EEE EE EE NN E EEE 17 POINT SINK OR SOURCE OF KNOWN STRENGTH cssssssssssssssseseccccccccecceeeeeaaaeassseseseeeeeeeeeeeeees 17 HORIZONTAL LINE SINK OR SOURCE OF KNOWN STRENGTH oooocccccnccnnonononnnnnnnnnnnonnnnnnnnnnnnononnnnos 18 CIRCULAR LEAKING POND OF KNOWN STRENGTH s sssssssseeeeccececcccccceeeaaeeesssssesseeeeeeeeeeeees 20 ACKNOWLEDGE IVE INT S Gs 21 ACKNOWLEDGEMENTS suse 22 TECHNICAL SUPPORT pe 22 FREQUENTLY ASKED QUESTIONS Luse 22 REFERENCES ss 25 APPENDIX A KRIGING WATER LEVELS WITH A REGIONAL LINEAR AND POINT LOGARITHMIC DRIFT GROUND WATER 2002 eeeoooooosessssvvvveeeeenssnnnnnnevseeeeee 27 Outline This document describes the KT3D H20 v2 0 programs which provide a customized version of the popular kriging program KT3D Deutsch and Journel 1992 that has been modified to include drift terms derived from the hydrologic sciences These drift terms are included in order to account for the influence of point line and circular boundaries such as wells
42. ceeded Men 3 4 UnconfinedSasc 2 Data Layers Hydraulic capture zones In the Part Track tab under Starting Loc Options select Custom regular grid and under Tracking Type select Multi Event Tracker ES Run Fart Track Define particle tracking parameters and click Run Part Track button After particle tracking is finished a capture ASCII grid file is generated This file contains an array of integers which represents the different extraction wells boundaries and other types of zones or sinks where a particle was removed from particle tracking KT3D_H20 converts those integers into zone an explanation shown in the MapWindow 21 legend By default particle pathlines shapefiles are not generated during hydraulic capture analysis This option can be selected by checking the Generate Particle Tracking Generate Particle Shapefiles box in the Part Track tab 95 St Capture Frequency map For Multi Event projects there is an additional option to calculate a capture frequency map This map describes the number of times a particle was removed at an extraction well compared to the number of events calculated 1 e the fraction of capture for each particle For example frequency of 0 5 indicates that during all the events for which capture zones were calculated the particle was captured by an extraction well 50 of the time This suggests that on the basis of the measured water le
43. cking routine to move the particles in accordance with the flow field and for the random walk to add a component of uncertainty in the simulated position of each particle As an additional test of Transient Tracker two additional simulations were performed using the same flow field For the first additional run Run 2 longitudinal dis persivity decreased by a factor of 10 and for Run 3 dispersion was not simulated Figure 5 The results are consistent with expectations Run 2 has a decreased longitudinal spread with the same transverse spreading and the third run is a simple translocation of the source in the uniform flow field according to advection alone 2 3 Verification Using Numerical Solutions Transient Tracker particle tracking results were also compared to MODPATH v4 3 Pollock 1994 and PATH3D Zheng 1992 A rectangular uniform grid two dimensional simulation was constructed Grid cells were 100 feet on each side The grid had 50 rows and 100 columns Boundary conditions consisted of three sections of general head boundaries around a portion of the perimeter and a well that switched from injection off to low pumping and then high pumping matching the initial injection rate over the course of four stress periods Figure 6 The first stress period was steady state followed by 100 days of no pumping 1000 days of low pumping and then 30000 days of high pumping Other model run parameters are summarized in the table below
44. cking is finished you will be prompted to enter the path and output shapefile name The output shapefile will be saved in the specified directory and added to the project map Note the grid you selected before running particle tracking the first time will remain active until you select a new grid There is no need to select the grid each time you run particle tracking 2 Multi event project Two types of tracking are available for Multi Event projects Multi Tera use event and Transient tracking Multi Event Tracker Multi Event In the Part Track tab under Tracking Type WEBER select Multi Event Define particle tracking parameters and click the Run Part Track button The Event Selector dialog will appear Select the appropriate event grid files and click OK KT3D H20 will perform particle tracking on each grid file individually using the specified particle tracking parameters for each event and also output files will be generated for each event Transient Tracker In the merre ae A Event Date GrdHle Mk me he eaten ee Deane paid meses End Time For Tran Tracker 5 20 2004 e and click the Run Part Track ES Run Part Track e button ki The Event a a 4 Sellect All A 18 19 2l 2 23 Selector dialog will appear The 95 25 27 28 29 column GridFile is populated with the corresponding event 25 default ASCII grid file names any grid files may be selected by right c
45. d as described in the previous section can now be used to generate a particle tracks Particle tracking is performed in KT3D H20 using TransientTracker Attachment 2 It supports the approximate evaluations of historic and future contaminant migration of hydraulic capture zones developed by pump and treat type remedies and other analyses that benefit from the ability to track particles on a surface The particle tracking utility has been adapted to use the program TransientTracker as a processing engine while KT3D H20 is used to generate ASCII input files and for post processing TransientTracker outputs KT3D_H20 OTT_Unconfined Grid Sett Krig Sett Krig Type Variograms Direction of Tracking v Tracking Type Starting Loc Options CEP v MuttyEvent Tracker v Show data To Run Screen Particle Tracking Press Shift X coord Column AX vi and Right Mouse click for particle starting location Y coord BEN y Part Track shapefile output type TEE Shapefile lv Particle Track ASCII Output File OM teeing cman et Particle Tracking Settings Hydraulic Cond Porosity Courant Number Sink Strength Max Time Steps 0 Step Size Max Time 35000 Output Frequency Vsmall Roerr Tiny Safety EPS All particle tracking settings are in the Part Track tab Here you can set particle starting locations tracking type tracking parameters and output type Setting pa
46. e Y Min kriging Y Max Total Particles e Quick screen particle tracking For single event projects hold down the Shift key cursor will change to the target shape and click with right mouse button at the particle starting location on the map The program will instantly run particle tracking using existing particle tracking parameters For Multi Event projects this option is only available using transient tracking In the Part Track tab select Transient Tracker As with single even projects hold down the shift key and right click on the starting location on the map The event selector dialog will appear Select the grids to be used in transient tracking The particle will be tracked along the selected grids according to the specified step size until the last date in the Event Selector Dialog End Time for Transient Tracker By default this is the current date More information on transient tracking is available in the attached Transient Tracker documentation Attachment 2 24 Running particle tracking l To run particle tracking for a single event project set up particle starting locations as described in the previous section Select particle tracking shapefile output type point or polyline and define particle tracking parameters Then from the Mapwindow legend select kriged grid file In the main KT3D H20 toolbar click the ES Run Part Track Run Part Track button After tra
47. e if and where a particle was removed from the particle tracking for any of the reasons listed above The value of this variable as written to capture out can be used to produce maps that illustrate the fate of the particles Current capabilities include the removal of particles that exit the domain e Not captured IREM 0 e At the bounds of the grid IREM 1 e At a 2D Recovery Well IREM 2 QTYPE R e At a 2D line sink sources IREM 3 e At a stagnation point IREM 5 or 6 e Beyond the maximum transport simulation time IREM 8 e Number of tracking steps exceeded IREM 9 e Internal stagnation point IREM 10 Non recovery wells are typically injection wells but may also be wells that are not pumping in a particular stress period but were simply left in the input file for con sistency The file capture out provides for each particle the starting location exit time exit coordinates exit row column and layer and the mechanism of exit An example of a portion of a capture out file is provided below 1 6161 9587 1761 6945 0 0000 14852 2305 3556 8680 947 477 2 5948 3987 1685 1856 0 0000 13742 2650 3557 3389 944 395 3 5626 3664 1414 9735 0 0000 11981 5765 3553 3730 953 438 4 5870 5205 1624 0371 0 0000 13106 5835 3550 3535 943 901 2 Program Verification Data Set Transient Tracker was verified using two analytical solutions and a set of numerical solutions of a two dimensional transient system 10 2 1
48. e set to 0 0 in the input file 1 4 Input Transient Tracker reads up to four types of input files The first one is the main input file Transient Iracker in and is required and must have the default name The other three types are Surfer grid files GRDFILES Well files WELFILES and Sink files LINEFILES All of these files are listed by name in Transient Tracker in 20 0 ft a Bilinear interpolation EA 0 0 tt 20 0 ft 30 0 ft b Linear log Kriging Figure 1 Example head surface near a pumping well red circle calculated using a bilinear interpolation and b linear log kriging EA 0 0 tt 20 0 ft 30 0 tt Figure 2 Example particle tracks using the linear log kriging approach The following table provides a summary of the variables required in the default in put file Transient Tracker in in the format required by the code The indices indicate the order in which the variables are listed in the file a new line for each successive index with some variables requiring multiple lines of input Text in lowercase bold are Character variables they need to be entered exactly as provided in the table followed by the variables indicated The input is free format entries do not need a specific spacing on each line and multiple entries on a line should be separated by one or more spaces Variables nerd NGRD EE 2 ncol NCOL nrow NROW xmn XMN ymn YMN 6 zmn ZMN 7 GRDFILES i WELFILES i L
49. eady state condition If this is not the case the rate of change in hydraulic gradients should approach zero Because the form of the underlying drift is assumed to apply to the entire dataset the drift model parameters are calculated from a global estimation of Z u Linear log kriging is performed using a selection of Fortran routines modified from U S Geological Survey Program Number K603 coded by Skriven and Karlinger 1977 F Q g gt p 5 Q 2 E 2 S Lag Distance Meters Figure 3 Measured data raw semivariogram Example Dataset Cape Cod Massachusetts Water levels measured in 32 wells of the Chemical Spili 10 CS 10 plume Massachusetts Military Reservation MMR Cape Cod Figure 1 monitoring well network were gridded using the approach detailed previously Numerous excellent discussions of remedial activities at MMR are available in the literature e g AFCEE 2000 and the MMR Web site at www mmr org The principal contaminants in the CS 10 plume are trichloroethene TCE and perchloroethene PCE and the selected remedy for the plume is pump and treat The CS 10 plume is within the Mashpee Pitted Plain MPP sediments which comprise well to poorly sorted fine to coarse grained sands forming a broad outwash plain that typically displays high hydraulic conductivities on the order of 2 X 10 m sec 15 m day or greater Hess et al 1992 Drawdowns resulting from pumping of CS 10 extract
50. ed use column selector dropdowns to select column for X and Y coordinate b Automated For projects using a 2D well drift there is an option to generate particles around each well in circular envelopes Enter the number of particles per envelope number of envelopes and radius of envelopes Number of Particles 10 For example if the radius of the first envelope is 50 ft then the Radius of Envelop 5D radius of the second is 100 the radius of the third envelope is Number of Envelopes 150 ft and so on This option can be executed only using 2 backward tracking 22 C Custom This option allows you to generate particle starting locations by drawing polylines or polygons or by selecting shapes from existing polygon shape files To open the Custom Particles dialog select Custom from the pull down menu next to Starting Loc l To draw a polyline Select the polyline lo a Y of Segments 3 tab on dialog menu In the of Particles per Segment Project Map left click to begin the line and right click to end it In the Custom Particles dialog type in the desired number of particles per segment The total number of particles will be calculated based on the number of segments in the polyline and the number of particles per segment After you have drawn the polyline and set the number of particles per segment click Add Particles Red dots will be converted to blue indicating that those
51. en the data import dialog Choose the appropriate input file and click OK The table to the left of the dialog will fill in with the input data Select the appropriate columns for coordinates drift term and head Note that Drift Term and Head must be numeric values and there is no event date column Single imported data set will be used for all kriged events Click OK to confirm completion 2D Circular pond Two dimensional circular pond drift can be added by clicking on 2D Circular Pond check box or select Edit gt 2D Pond Drift The 2D Pond Drift dialog will appear 2D Pond Drift gt x Coord Y Coord Radius Strenght Drift Term Rag Imported Data has 1 12623484 i e izszssi3 86 pp 10 gzz Jer ft Bl 252307 ess pf kh mb Hide Data Ca O Header row No Header Row E AAA A A Y Head Drift Date ie 4 es1012 1 1 284am1888 Zeer 1998 4 12523525 660219 5 12623566 659740 6 fr2s2sesefessero 1 1 2evan 1998 8 12623714 65s307 1 1 284an1998 8 12623307 658039 1 1 28van199 10 12623020 fes8ro2ft 1 28van1988 Click the Show Data button to open the data import dialog Choose the appropriate input file and click OK The table to the left of the dialog will fill in with the input data Select the appropriate columns for coordinates radius strength and drift term OK to confirm completion 13 Setting variogram parameters At the Variograms
52. er 1 1 Background Particle tracking has been implemented in Transient Tracker to support approximate evaluations of historic and future contaminant migration of hydraulic capture zones developed by pump and treat type remedies and other analyses that benefit from the ability to track particles on a surface Inputs required to execute particle tracking using TransientTracker are described in the following section The particle track ing implemented in Transient Tracker is currently only compatible with 2 D surfaces which must be provided to Transient Tracker as a formatted input Particle tracking uncertainty associated with the physical process of hydrody namic dispersion and mixing is incorporated through a random walk component The random walk movements are added to the advective displacements providing an indication of the expected uncertainty in particle location due to dispersion Larger numbers of particles will provide a better representation of the potential for plume spreading due to dispersion but will add significantly to computation time 1 2 Approach Particle tracking is implemented using the fourth order Runge Kutta RK4 Press et al 1992 numerical integration particle tracking scheme calculated upon hy draulic head surfaces that have been generated using any number of methods including analytical solutions interpolation of observed values or a numerical simulation such as MODFLOW McDonald and H
53. erse Dipsersivity L Initial Slug Mass 11 2000 1500 A Analytica s MUDOFAA ea 4 rameni racker 1 rd int E 1000 i 500 20 100 40 60 5 tarhng Distance From Well meters Figure 3 Travel time to reach pumping well calculated using 1 analytical solution 2 MODPATH and 3 Transient Tracker Using an assumed value of hydraulic conductivity equal to 100 0 a Surfer grid file was created with the same domain extent and grid resolution as the BRICK solution The piezometric surface generated using a gradient of 7 5 E 04 with the high values of piezometric surface along the left hand boundary X 50 0 Transient Tracker was run with the resulting Surfer Grid file using 1681 particles a square of 41 x 41 particles and dispersivity values matching the BRICK values The file TransientTracker in is provided below Input file for TransientTracker benchtesting against BRICK ngrd 1 ncol 551 nrow 201 xmn 50 00 ymn 100 00 zmn Q Grid File information using 1 line for each stress period fabgrid551x201 grd nowells dat nosinks dat 1000 Tracking information 1 100000 100 0 0 3 10 0 1 50 1 1 30000 10 0 0 1 0 1 e 3 1 e 6 0 8 1 e 6 1 0e 3 1 0 O Particle Locations 1681 12 nparticles 1681 5 00 5 00 4 75 5 00 4 50 5 00 4 25 5 00 Keep input continues until particle 1681 The results depicted in Figure 4 demonstrate the ability of the particle tra
54. ersion 3 0 Point Sink or Source of Known Strength The KT3D_H20 suite of programs is supplied together with an example multiple pumping well data set as described in the paper by Tonkin and Larson 2002 and output files in Surfer format Verification 2DWells srf showing the resulting water level surface and example particle tracks Since these results are provided in Tonkin and Larson 2002 they are not included in this documentation This example data set includes five extraction wells and backward particle tracking using concentric circle of particles placed around each well this example data set is provided with the program The first table shows the entries in the kriging input PAR file the second table shows the entries in the pumping data file SDWELL DAT Parameters for KT3D H20 OOOO OO K KK K KK K START OF PARAMETERS test dat 12030 1 0e21 1 0e21 0 none dat 12030 0 KT3D dbg KT3D out 201 857000 25 251 238000 25 1 1 1 1 1 1 30 40 0 20000 0 20000 0 20 0 00 0 0 0 0 1 0 0 110000000100 0 none dat file with data columns for X Y Z var sec var trimming limits option O grid l cross 2 jackknife file with jackknife data columns for X Y Z vr and sec var debugging level 0 1 2 3 file for debugging output file for kriged output nx xmn xSiZ ny ymn ysiz nz zmn Zsiz x y and z block discretization min max data for kriging Y max per octant 0 gt no
55. es can be edited on Grid Extent dialog Once you are satisfied with grid extent click OK x A Grid Extand Setting Kriging parameters To set kriging parameters select the Krig Sett tab Three kriging options are available in the pull down menu regular kriging grid of points Cross validation and Jackknife In cross validation actual data are dropped one at a time and re estimated from some of the remaining neighboring data Each datum is replaced in the data set once it has been re estimated The term jackknife applies to resampling without replacement 1 e when alternative sets of data from other values are re estimated nonoverlapping data sets For detailed information of kriging parameters a A roar Fe bT P Grid Sett KT3D_H20 UnconfinedR a Krig Sett Ee a gt tochasto ail Jackknife Options File with Jackknife data Z coord Search Options Number of Data dais be Kriging Number sh discr point for a bloc Columns for X coord Y coord Variable Ext Drift Var Min Ma Search FEE for Radius search ellipsoid X direction 223 Max number to retain from octant il Y direction He ent on this tab please refer to the GSLIB User s Guide book or visit the website at http www gslib com gslib_help kt3d html 10 Selecting kriging types and drifts To set kriging type trend indicator or drift options click on the Krig Type tab
56. es the principal physical processes that govern ground water flow and ultimately govern the autocorrelation of ground water elevation data This approach produces maps of contoured water levels that more realistically represent physical conditions and allow for improved interpretation of measured water level data by including features and infor mation known to be present Additional benefits include an improved estimate of the regional background hydraulic gradient and generation of an approximately flow conserved grid suitable for two dimensional particle tracking Introduction Kriging is widely used throughout the hydrog ologic discipline as the preferred method for constructing gridded hydrogeologic datasets suitable for contouring Kriging was introduced as a least squares estimator that improved on methods such as distance weighting or polynomial interpolation for which weighting was a determinant Delhomme 1978 An advantage of kriging is that in the absence of measurement error it is an exact interpolator at measurement points In addition kriging yields both estimated values and estimate variances Skrivan and Karlinger 1977 Kriging is ideally an investigative and iterative process including devel opment and fitting of an analytical function representing the under lying trend or drift where evidence exists for such and development of a semivariogram to describe the pattern of residuals measured data minus drift Volpi and Gambola
57. founded as the drifts described in this document The drift was derived on the basis of an infinite fully penetrating line sink e in a confined aquifer there is no curvature of the water table and the slope towards the boundary feature is planar e in an unconfined aquifer with no recharge the curvature of the water table approximates a quadratic This form of drift term is implemented as 1 h A r h a Where hij is the elevation of the potentiometric surface at location 1 a is a scalar that is a function of T recharge and aquifer type p is a power term which is typically specified as 0 5 but is a function of the penetration of the feature r is the distance of location 1 3 from the boundary feature and hz is the elevation of the boundary feature The user can provide an arbitrary power for the drift ranging from 1 0 e linear approximating the simple confined case to 0 5 1 e quadratic approximating the second case Note that the drift does not presently account for a slope in this feature e g a bed slope in a river across the data domain NOTE In the current version of KT3D H20 this drift term is disabled Please contact matt sspa com if this drift may suite your needs References Brochu Y and Marcotte D 2003 A simple approach to account for radial flow and boundary conditions when kriging hydraulic head fields for confined aquifers Mathematical Geology Vol 35 No 2 February 2003 Chi
58. ft term drop down menu will generate number one 1 for all wells as a drift term If you are running a multi event project an additional field called Event is available The events should be a Julian date and should correspond to the events in your water level input data Recovery column values True False are used in particle tracking procedure to define if well is used to determine capture zones analysis default value is True Once imported the well drift data may be edited in the Well Drift dialog To exclude the well drift select the whole row by clicking on the row number and press Delete key on your keyboard Confirm completion of well drift data editing by clicking OK Well drift data can be edited or changed at any time by selecting Edit from the KT3D H20 main 2d Well Drift 2D Line Drift toolbar and then selecting 2D Well Drift from the pull down menu 2D Horizontal line sink source drift To add the effect of horizontal linear features click on 2D Line Sink check box or select Edit gt 2D Line Drift The 2D Line Drift dialog will appear 12 20 Line Drift 4 Coord Tv Coord Line Drift Term Head KE SO Pess Jes 1 oo J 12623592 fi AE E EE Z lo l L l ancel Hide Data Imported Data has Header row No Header Row P 10254T ask 011 Ot Story CordowaiKt3D ic e pazar 1 1n 1 I Click the Show Data button to op
59. have the following definitions NLIN Number of line segments to be read in the file Must be less than 100 which is hardwired into the code as MAXNLIN ind i Indicator of line sink source feature type 1 river with a const head value 2 horiz well with const Q in Q out value for the line feature Head when lind 1 river when en dum 1 5 Output Transient Tracker produces two output files the particle tracks ptrack out and the capture locations of each particle capture out Both ptrack out and capture out are formatted ASCII files that can easily be imported by a plotting package such as Surfer The file ptrack out provides a listing of the particle locations x y time particle number with each transport step or multiple of transport steps depending on the value of NOUT A sample of the first few lines of a typical ptrack out file is provided below 0 374760000000E 04 0 413894000000E 04 0 000000000000E 00 1 0 374879680903E 04 0 413927856838E 04 0 200000000000E 00 1 0 374733118239E 04 0 413823623645E 04 0 100000000000E 01 1 Transient Tracker includes functionality for removing particles at the margins of the grid domain at stagnation zones at sinks when forward tracking The program records the fate of particles in an ASCII summary file called capture out The contents of this file can be manipulated to illustrate capture zones The program uses an integer variable IREM to indicat
60. he following definitions X location of point s 1 Ly 1 Y location of point s 1 Ldrift 1 Indicator of line sink source drift term Lval 1 Head value for the line feature Event date in format of Julian Date Pond Drift Data Pond Drift File This file defines the locations and characteristics of circular and should be provided in the following format Variables l Header Line 2 DX i pY i pRadius i pStrenght i pDrift where this line is repeated by number of ponds The parameters listed above have the following definitions pX 1 Pond center X coordinate pY 1 Pond center Y coordinate pR 1 Pond Radius pStrenght 1 Pond Strength pDrift 1 Indicator of pond drift term For detailed information about each input parameter please refer to the Attachment 1 32 Appendix B Binary File Formats Kriging Binary file kbf and Capture Binary file cbf have identical structure for the practical reasons they have different extensions Binary file has one header section and unlimited grid array sections Data types used in binary files long 32 bit signed integer double 64 bit double precision floating point value Text I bit Header section describes dimension of 3D array and contains all the data for defining the grid X double X coordinate of the lower left corner of the grid BlankValue double nodes are blanked 1f equal to this value Text Some file description 50 cha
61. he row the list of Z values continues with the next higher row until all the rows of Z values have been included The general format of an ASCII grid file 1s ncolsncol number of columns in the grid EEE oS eT eee re eee NE coordinate of the lower left center of the grid cell coordinate of the lower left center of the grid cell dx xsize The grid values are stored in row major order starting with the maximum coordinate The first grid value in the grid file corresponds to the upper left corner of the map The second grid value is the next adjacent grid node in the same row the same Y coordinate but the next higher X coordinate 35 Attachment 1 KT3D_H20 v3 0 A Program for Kriging Water Level Data using Hydrologic Drift Terms Theoretical Documentation KT3D H20 v3 0 A Program for Kriging Water Level Data using Hydrologic Drift Terms Time of Travel Days SE 0 to 100 100 to 200 G 200 to 300 300 to 400 J e va Ya fy Heo fe a T Theoretical Documentation 5 5 Papadopulos amp Associates Inc DESCRIPTION OF THE KT3D H20 PROGRAM SUITE VEN NNN 4 BACKGROUND vvs 5 UNIVERSAL KRIGNG suv 5 EA PERO ER EK ee tee 8 ADDITIONAL DRIFT TERMS IMPLEMENTED IN KT3D H20 eesesosessssvsesssvsessssssessesseee 9 1 POINT SINK OR SOURCE OF KNOWN STRENGTH sevvvvevnnksbesrennnnanenenennannenervnsnakebegnennnnnnenenenennnekete 9 2 HORIZONTAL LINE SINK OR SOURCE OF KNOWN STRENGTH ooooccc
62. hecks for co located wells and should identify these and terminate with an error message reporting the conflict s NOTE Every effort should be made to ensure there are no collocation conflicts either extraction wells at the same location as observation wells or observation wells at the same location as an estimation point This can be done in one of two ways 1 the user should check these conflicts will not occur 2 by pragmatically by simply adding some small delta d to the observation well location coordinates The latter pragmatic approach of adding some delta d value to the X or Y of the observation points should in the majority of instances avoid these conflicts without affecting results or their interpretation however the magnitude of the value delta d will be case specific I get a division by zero error but have checked all my data and have no collocated wells or points This can occur where for example the data set contains one extraction well and one injection well and these wells form a recirculation system with extraction equaling injection This can be pragmatically overcome by adding a small delta q to one of the wells Again this is a pragmatic solution and delta q is case specific Notes on an Arbitrary 2 D Polyline Boundary A drift was incorporated in KT3D_H20 at one time to provide a general method for representing fairly distant rivers and other extended length features This approach is not as rigorously
63. hen check Overwrite Existing Files If this option 1s selected the UI will generate and use default Surfer grid filenames and save them in the project directory The default file name is constructed as project file name event date for example newproject 28 Jan 1998 grd Surfer grid files can also be automatically generated during Multi Event kriging To do this go to the Multi Event tab check Generate Surfer grid file during multi event run Note this option must be selected before kriging is performed Importing kriging results Kriging results can be imported at any Event Selector Kriging Event GridHi time by selecting Plot Color Flood For a nales 23 Jan 1998 Mulit Event projects a Event Selector 2 E 27Feb1998_ OTT_Uncontined_27 Feb 1998 asc 3 O 23Mar1998 OTT Unconfined 23 Mar 1998 asc dialog will appear If all files have LE 07 unconfined 07 Apr 1998 ssc sjefer for Uncorfned 19May 1558050 default file names the Gridfile cell next E 2er OT Unconfined 25un 1998 ase 7 E1088 OTT Uncorfined 10u 1988as to each event will be populated with the H 07A01958 T_Unconfined_07 Aug 1998 ase g C 10Sep 1998 corresponding ASCII grid file name Lee asc Alternately you can select any MM ASCII grid file to plot by right clicking in the Gridfile cell next to the Event A file selector dialog will appear Choose the appropriate g
64. icator boolean if well is used for Indicator boolean if well is used for recovery recovery Event Date Optional Used for particle tracking only Radius of each pond Sink strength for each pond Drift term flag for each pond Importing data To import new data select Grid Sett tab and click Pick a worksheet on the button labeled Show Data then click the mpot tew Data button or File Import New Data Set Select the input data file type KT3D H20 supports importing data from Microsoft Excel xls xlsx Xlsb and xlsm files Microsoft Access mdb and accdb files ESRI ShapeFiles shp and ASCII txt or dat files with values separated by space comma or tab If an Excel or Access file is chosen then the worksheet table query selector dialog will appear Select the appropriate worksheet table query then click OK Your data should appear in the data table Imported Data has Header row No Header Row gt Import New Data Append New Data X StPIng3 ft Y StPIn83 ft water Illa fv 12621476 73 636 83 12621425 63 635 17 Jalan lemen fen 6 A 12621818 1 632 95 12621774 63 619 67 8 e 12623215 19 609 72 lejanas mes os 118 12621513 03 637 95 lt m i gt By default the Data Has Header Row button is selected if your data has no header row click the No Header Row radio button Setting grid parameters To set grid para
65. ift model The gridded ground water levels calculated with no drift the linear drift and the linear log drift formed the basis of particle track ing analyses using Path3D Zheng 1992 to delineate the well capture zones Figure 6 The saturated thickness was simulated for a confined single layer isotropic homogeneous aquifer of 60 m Comparison of the resulting maps indicates 1 In areas of high data control and low stress consistent gradi ents particle tracks are similar 2 Inareas of high data control and a single stress e g in the area of steep gradients close to O3EW2104 particle tracks of the linear and linear log drift maps are quite similar 3 In areas of fairly high data control and more than one stress e g in the area of complex gradients close to O3EW2105 and 03EW2106 the linear and linear log drift particle tracks dif fer markedly In particular the capture zone of 03EW2105 appears grossly exaggerated in the linear drift map because the data density is insufficient to account for the complex shape of the ground water surface near two extraction wells 4 In areas of low data control near single or multiple stresses the linear and linear log drift particle tracks differ markedly In par ticular near 03EW2102 and 03EW2106 the linear drift map shows no drawdown and consequently no particles are a 500m 1000m Figure 6 Delineation of well capture zones by particle tracking analyses a no
66. inear drift models by esti mating the value of the drift component of Equation 1 at each suppressed point in turn and summing the squared differences The calculated sum of squared differences are 0 67 and 0 97 m for the linear log and linear drift models respectively The scattergram Figure 15 and rank percentile plot Figure 16 further support the conclusion that the linear log drift model is a better model or pre dictor of the measured water levels As outlined in Gaganis and Smith 2001 errors arising from the imperfect mathematical representation of the structure of a hydrologic system i e model error are not random but rather systematic A review of model error may elucidate the form of this systematic error or model bias For the Cape Cod dataset the squared residuals calculated from the jackknifing approach have been mapped in Figure 17 Where data are available adjacent to the extraction wells the linear log error is less than half the linear error indicated by a square away from the extraction wells the pattern appears more random This simple comparison supports the intuitive conclusion that residuals from the linear drift model are biased high adjacent to the extraction wells where the form of the drift model is unable to represent the shape of the depressed poten tiometric surface Further analysis of the residuals might indicate that their mag nitude and distribution reflect deviations of field conditions from
67. ing water levels with a regional linear and point logarithmic drift Ground Water 40 2 185 193 March April Volpi G and Gambolati G 1978 On the use of a main trend for the kriging technique in hydrology Advances in Water Resources 1 345 349 Zheng C 1992 PATH3D A Groundwater Path and Travel Time Simulator Version 3 0 S S Papadopulos amp Associates Inc Bethesda Maryland Appendix A Kriging Water Levels with a Regional linear and Point logarithmic Drift Ground Water 2002 Kriging Water Levels with a Regional Linear and Point Logarithmic Drift by Matthew J Tonkin and Steven P Larson Abstract Ground water levels measured in the vicinity of pumping wells are kriged using a regional linear and point logarithmic drift the latter derived from the approximation to the Theis equation for drawdown in response to a pumping well Kriging is widely used throughout the hydrogeologic discipline most commonly as the preferred method for constructing gridded hydrogeologic datasets suitable for contouring Residuals arising from using the most common linear drift to krige water levels in the vicinity of extrac tion wells often indicate large local departures from the linear drift which correlate with areas of drawdown The combined regional linear and point logarithmic drift accounts for these drawdowns using a logarithmic approximation for the curvature of the poten tiometric surface The drift model approximat
68. ion wells typically do not exceed 1 to 1 5 m of a total saturated thickness aver aging 60 m Assumptions underlying the Theis approximation are considered to be fairly well adhered to Water levels selected for this study were measured in 1999 at wells in the upgradient area of the plume where four extraction wells were being operated to remove ground water contaminated with TCE and PCE The monitoring network in this area is fairly dense with monitoring well separations on the order of a few tens to a few hundred meters Nineteen monitoring wells in the middle of the study area are shown in Figure 2 the remaining wells lie to the south and west of this local scale map Water level contours are shown only for the zoom area because this is the area of interest for deter mining extraction well capture zones At the time water levels were collected for this study two extraction wells had monitoring wells within 20 m for use in aquifer tests For the remaining extrac tion wells the nearest monitoring wells were 150 m away In the case of one extraction well 03EW2102 the water level in the near est monitoring well was not measured and the nearest water level measurement was at a distance of 300 m The raw data semivar iogram is shown in Figure 3 The parabolic behavior of the raw semi variogram is a strong diagnostic indicator of the existence of a trend in the data Clark and Harper 2000 Initially point kriging was performed for
69. ithout any pumping lasted 100 days and the third lasting 1000 days had a pumping rate of 20 gpm The fourth and final stress period pumped at a rate of 250 gpm and had a 30 000 day duration allowing plenty of time for any particles to complete their travel A portion of the TransientTracker input file TransientTracker in used in the verification runs is reproduced below Only the first five particles are listed and some parameters such as dispersivity were modified between runs Input file ngrd 13 ncol 100 nrow 50 xmn 50 ymn 50 zmn 0 Grid File information using 1 line for each stress period vista3_T02000_0 grd nowells dat nosinks dat 2000 0 vista3_T02018_6 grd nowells dat nosinks dat 2018 vista3_T02041_0 grd nowells dat nosinks dat 2041 vista3 T02067 8 grd nowells dat nosinks dat 2067 vista3_T02100_0 grd nowells dat nosinks dat 2100 vista3_T02286_3 grd nowells dat nosinks dat 2286 vista3_T02509_8 grd nowells dat nosinks dat 2509 vista3_T02778_1 grd nowells dat nosinks dat 2778 vista3_T03100_0 grd nowells dat nosinks dat 3100 vista3 T08688 7 grd wells dat nosinks dat 8688 7 vista3_T15395_1 grd wells dat nosinks dat 15395 1 vista3 T23442 8 grd wells dat nosinks dat 22442 8 vista3 T33100 0 grd wells dat nosinks dat 33100 1 Tracking information 1 900000 100 0 100 0 20 50 1 1 33100 1 2 5 0 50 1 e 3 1 e 6 0 8 1 e 6 1 0e 31 0 0 Particle Locations 100 nparticles 100 3 74760E 03 4 13894E 03 P0001 3
70. itoring locations table shows the entries in the kriging input PAR file the second table shows the entries in the line segment file 2DSINK DAT Images from the results are provided as Figure 5 The slight discrepancy between the MODFLOW model and KT3d_H20 results 1s due to the MODFLOW discretization and the proximity of the constant head boundary Parameters for KT3D KKK K K K K K K K K K K K K K K K K START OF PARAMETERS wl 2DSINK DAT 120 3 0 1 0e21 1 0e21 0 none dat 120 3 0 0 kt3d dbg kt3d out 101 6100 01 50 101 6100 01 50 1 1 1 1 1 1 40 40 0 20000 0 20000 0 1 0 0 0 0 0 0 0 1 0 0 110000000010 1 none dat 4 1 0 0 1 5 0 0 0 0 0 0 0 file with data columns for X Y Z var sec var trimming limits option O grid 1 cross 2 jackknife file with jackknife data Y columns for X Y Z vr and sec var debugging level 0 1 2 3 file for debugging output file for kriged output nx xmn xsiz ny ymn ysiz nz zmn zsiz x y and z block discretization min max data for kriging Y max per octant 0 gt not used maximum search radii angles for search ellipsoid 0 SK 1 OK 2 non st SK 3 exdrift drift X y Z XX VY ZZ XY XZ ZY Q R PP 0 variable 1 estimate trend gridded file with drift mean column number in gridded file nst nugget effect it cc ang1 ang2 ang3 15000 0 15000 0 1 0 Va hmax a_hmin vert 1 100 100 0 2 1 0 1 50 1 tracki
71. ium L T NOTE this value must be in units that are consistent with the flow simulations that generated the piezometric surface that was gridded using Surfer Porosity of the porous medium STEP Transport step size for moving particles APART o oo XPRAD Placeholder value for future use NOUT Transport step interval for output e g NOUT 5 will produce output every 5th transport step MAXTIME ALPL Longitudinal dispersivity L NOTE this value must be in units that are consistent with the flow simulations that generated the piezometric surface that was gridded using Surfer Transverse dispersivity L NOTE this value must be in units that are consistent with the flow simulations that generated the piezometric surface that was gridded using Surfer ALPT PORZ Flag to indicate which formulation of the random walk dispersion approximation is used PORZ 0 for Prickett et al 1981 or PORZ 1 for Zheng and Bennett 2002 ROERR Round off error cutoff for Runge Kutta integration TINY Stagnation and minimum tracking time criterion for Runge Kutta integration recommended 1 0 E 10 Stepsize adjustment criterion for Runge Kutta integration recommended 0 80 EPS Error criterion scaling factor for Runge Kutta integration recommended 1 0 E 06 Ni VSMALL Placeholder value for future use recommended SQRT EPS COURANT Particle step control If the updated particle location moves a
72. l grids must have the same dimen sions and origins Formatting instructions for creating Surfer ASCII files is includedin Appendix A of this manual WELFILES i The files defining the locations and characteristics of each well are simple ASCII files and provide information in the following format Variable NWELLS qxx i qyy i qqq i qrad i idtwell i qtype i wellname i where this line is repeated NWELLS times The parameters listed above have the following definitions NWELLS Specifies the number of wells files that are active during this timestep the wells that influenced the current grid file qxx i X coordinate of well i Y coordinate of well i Pumping rate of well i for the current timestep stability of the final particle transport steps idtwell A well id label Specify the well as recovery R or not recovery NR wellname i A name for the well LINEFILES i These files define the locations and characteristics of sink line seg ments They are simple ASCII files and provide information in the fol qrad i Well bore radius Used to capture the particles as they approach the well In some instances especially with wells creating a very sharp cone of depression increasing this number beyond the actual well bore radius may help with i lowing format NOTE Items 2 and 3 are repeated NLIN times If NLIN lt 0 then only 2 is repeated NLIN times The parameters listed above
73. larly important in down gradi ent areas where constraint of the capture zone by determination of the stagnation zone can be critical All of these factors make con touring of measured ground water elevations typically unsuitable for delimiting the capture zone of a pumping well An approach for gridding ground water level data is presented here Application of this method produces contoured data maps that can improve interpretation of measured water level data A combined regional linear and point logarithmic drift is employed to specifi cally account for drawdown and mounding in the vicinity of extrac tion and injection wells using a logarithmic approximation for the curvature of the potentiometric surface The point logarithmic drift is derived from the approximation to the Theis equation for draw down due to a pumping well Examples are provided comparing con toured ground water levels measured in the vicinity of pumping wells kriged using no drift linear drift and the new combined drift models Data requirements for the new method are limited to knowledge of pumping activities including location and rates and knowledge of the geographic coordinates of monitoring wells Primary benefits from application of this method include improved estimates of the regional background hydraulic gradient and gen eration of a gridded dataset suitable for two dimensional particle tracking In m Inclusion of a logarithmic component in
74. les J and P Delfiner 1999 Geostatistics Modeling Spatial Uncertainty New York John Wiley amp Sons Deutsch C and Journel A 1992 GSLIB Geostatistical Software Library and User s Guide Oxford University Press 340 pp Ferris J G D B Knowles R H Brown and R W Stallman 1962 Theory of aquifer tests U S Geological Survey Water Supply Paper 1536 E Fitts C 2004 TWODAN Manual Fitts Geosolutions Scarborough Maine McDonald M G and Harbaugh A W 1988 A modular three dimensional finite difference ground water flow model U S Geological Survey Techniques of Water Resources Investigations book 6 chap Al 586 p Pollock D W 1994 User s Guide for MODPATH MODPATH PLOT Version 3 A particle tracking post processing package for MODFLOW the U S Geological Survey finite difference ground water flow model U S Geological Survey Open File Report 94 464 234 p Press W H B P Flannery S A Teukolsky and W T Vetterling 1996 Numerical Recipes in Fortran 90 Vol 2 2nd edn Cambridge University Press Cambridge Reilly T E O L Franke and G D Bennett 1987 The principal of superposition and its application in ground water hydraulics USGS Techniques of Water Resources Investigations of the United States Geological Survey Book 3 Chapter B6 Strack O D L 1989 Groundwater Mechanics Prentice Hall Englewood Cliffs New Jersey Tonkin M J and Larson S P 2002 Krig
75. licking on the event GridFile cell Check the appropriate events kriged grid files The bottom of the Event Selector dialog contains an event called End Time for Transient Tracker Enter the date that transient tracking stops By default this is the current date This date may be changed manually or may be chosen from the calendar To view the calendar click slowly two times on the End Time for Transient Tracker Event Date cell Transient tracking will be performed along the selected grids from the first date selected to the specified end date Step size must be specified in the particle tracking parameters and must be in units of days For more information on the transient tracking process see the attached Transient Tracker documentation Attachment 2 26 Hydraulic Capture Zone analysis Hydraulic Capture Zone analysis records the fate of particles during tracking simulation TransientTracker Attachment 2 includes functionality for removing particles at the margins of the grid domain at stagnation zones at sinks when forward tracking The program records the fate of particles in an ASCII summary file The contents of this file is used by KT3D H20 to illustrate capture zones This section describes how to use KT3D H20 to generate capture zone maps and capture frequency maps Legend EM UnconfinedS UnconfinedS_WD shp EY UnconfinedS_captureasc El Internal Stagnation Boundary El Stagnation gradient 0 Nptp ex
76. meters click on the Grid Sett tab in the main menu Parameters are set in the Input Output Options section Input options for both single event xpar and multi event xpars projects include XCoord YCoord Variable and Well Name By default KT3D_H20 assigns the first column in your input data as X coordinate second as Y coordinate third as kriging variable and fourth as well name Any input option column reference can be changed using the corresponding drop down menus For single event projects there is an additional option for External Drift Variable This column is not assigned by default and must be selected by the user Kriging with External drift is not supported in Multi Event projects For Multi Event projects instead of External Drift Variable there is an option for Event date This column is not assigned by default and must be specified by the user The data in this column must be in the form of a Julian date e g 1 1 2008 or January 1 2008 Grid extent can be updated in three ways l Entering values for Xmin Xmax Y min and Ymax manually P By clicking the ESTE button The program will analyze all values for X and Y coordinates of your input data and assigns minimum and maximum values for grid extent 3 By clicking the button You can generate the grid extent by drawing rectangle on the project map Left mouse click to the start drawing and right mouse click to end drawing Grid extent coordinat
77. mpling event To create a new project At the KT3D H20 main menu select File New A dialog will open prompting you for a folder name file name and project type Select the folder where all data will be stored then enter the project file name For project type select KT3D H20 single event XPAR File xpar for a single event project or KT3D_H20 multi event XPARS File xpars for a multi event project Then click Save Select the PARAMETER File Look in amp 2007 vi gt 2 fe Documents La Desktop My Documents eL My Computer gt File name OTT_2007xpars twork KT3D_H20 multi event XPARS File xpars My Netw Files of type KT30_H20 single event XFAR File xpar KT3D_H20 multi event XPARS File xpars To open an existing project In the KT3D H20 main menu select File Open Navigate to the appropriate folder and choose the correct file type xpar or xpars Your project name should appear in the window Select 1t and click Open Kriging to Generate a Grid Preparing data The following table lists the input parameters for KT3D H20 and generate a groundwater elevation grid map Appendix A describes the file formats Minimum Requirements Input type Supp sli E te ype Required components BS xpar file single event kriging xpars multi event kriging X Y coordinate of each location X Y coordinate of each location XY
78. name or directory was anything other than the default assigned by the UI then it is necessary to select the grid file manually To do this right click in the event GridFile cell You will be prompted to select another ASCII grid file which will be used for contouring in that Event Select desired events and click OK Contour shapefiles will be created for each event See Single Event Contouring for a full description of the contouring process Kriging output results also can be viewed by plotting nodal values Select Plot then Kriged Nodal Values select event and UI will generate point shape file with X and Y coordinate row column and kriged value at every node of your grid 17 Exporting kriging results Kriging results can be exported as a binary file kbf To do that select File Export KT3D H20 Binary file for file format see Appendix B Then in file type dropdown menu select KT3D_H20 Kriging Binary File kbf Enter the file name For Multi Event projects the Event Selector Dialog will appear Select event grid files you wish to export To export kriging results as a Surfer ASCII grid file select File Export ASCII Surfer Grid For a Multi Event project the Event selector dialog box will appear Select the Event grid files you wish to export For each event you will be prompted to enter the Surfer ASCII grid file name and location To skip this step click on Tools Project Settings t
79. neral not be used as observations The kriging code as currently written does not account for linear non linear well losses at extraction wells and hence the drift coefficients and map will be biased by these effects if in fact a division by zero error 1s not encountered first see below There are plans to add an additional drift term to account for linear well losses during the kriging as an additional drift term Please write to matt sspa com if you feel this drift term would be valuable to your needs The code reports a division by zero error upon execution Check that none of your extraction injection wells and observation monitoring wells are collocated i e have the same X and Y coordinates This will cause a division by zero error in the estimation of the drift terms since the separation distance is zero The current version of the kriging program checks for co located wells and should identify these and terminate with an error message The code reports NAN the Fortran not a number flag for an estimation point and or for a lagrange multiplier Check that none of your estimation points 1 e a node point for which we were asking the code to give an estimate and observation monitoring wells are collocated 1 e have the same X and Y coordinates This may cause an error in estimating the kriging weights under some circumstances since the separation distance is zero The current version of the kriging program c
80. nft dominates the contour pattern and further differences 188 M J Tonkin S P Larson GROUND WATER 40 no 2 185 193 between the linear and linear log drift maps are apparent Water level contours constructed using the linear log drift are concave to the extraction wells for some distance away from each extraction well The concavity decreases with distance from each extraction well This pattern is expected due to drawdown in response to pumping Water level contours calculated using the linear drift are concave close to each extraction well but the concavity is less defined far ther from the wells and the contours display the underlying linear drift This comparison suggests that kriging with a linear drift may result in a poor approximation of the underlying trend or regional gradient Although the scattergrams are at first glance indistin guishable Figure 5 on closer inspection the linear log drift esti mates squares are typically closer to the line of equality than the linear drift estimates circles This condition occurs largely from systematic typically by design bias in the location of monitoring wells close to extraction and injection wells and the tendency of the universal kriging routine to spread residuals error from the drift calculation throughout the gridded domain The sum of squared dif ferences for the two models differs by 50 in this case 0 5 m for the linear log drift model and 0 78 m for the linear dr
81. ng iback nptp hydcond porosity stepsize nparticles xprad nrads l e 4 1 e 10 0 80 1 e 6 1 e 3 roerr tiny safety eps vsmall note the code knows if particle tracking has been selected by an integer flag passed from the VB GUI to the KT3D_H20 DLL 2 7145 00 10270 00 9845 00 10270 00 10420 00 7595 00 10420 00 8295 00 Circular Leaking Pond of Known Strength Example data including water elevations and pond drift parameters are listed in the tables below Output files showing the resulting water level surface are supplied in Surfer format CircDriftEx srf S Images from the results are shown here Circular leaking pond of known strength a Pond with known infiltration rate b MODFLOW c Ordinary kriging with no pond drift d Kriging with pond drift Blue points indicate monitoring locations Data Used for Verification of KT3D_H20 Circular Pond Drift Well Name 100 887305 100 774772 100 981328 102 713499 101 36511 100 935022 101 00069 101 181256 102 583003 100 851355 100 989186 101 121289 101 221638 100 866058 101 236196 101 797811 100 91872 101 062477 101 435422 101 472925 Drift Parameters Used for Verification of KT3D_H20 Circular Pond Drift Strength Drift Term 10000 10000 Acknowledgements We offer sincere gratitude to Charles Fitts of Fitts Solutions ME for his invaluable guidance when we encountered difficulties programming the line
82. ntly 13 integers for the nine original drifts plus four additional drifts No options available to KT3D have been disabled to make KT3D_H20 Array size limitations as listed by the dimensions in the KT3D INC file provided with GSLIB are adhered to in compiling KT3D_H20 Significant arrays added to KT3D_H20 in adding the kriging and particle tracking functionality are allocatable however and should not be exceeded unless the program encounters problems allocating the memory KT3D H20 is compiled in single precision to reduce memory requirements In several tests comparison of grids and particle tracks calculated using single precision and double precision codes showed no noticeable improvement using double precision However if you encounter unsatisfactory results that may be linked to precision in particular if you encounter problems with particle tracking that could not be improved by modifying input options a double precision compiled version of the code can be provided upon request Additional Drift Terms Implemented in KT3D H20 Presently four drift terms have been added to KT3D H20 beyond those included in the original KT3D program Three of these drifts are only compatible with kriging of water levels in two dimensions 2 D One of these drifts is compatible with kriging of water levels in 3 D The first of these drifts to be developed the linear log drift is described first Subsequently the additional drift terms
83. ocation where the file will be saved By default this is the project directory Once you click Save the shapefile will be displayed in the MapWindow project 16 Multi Event kriging To run kriging click the button The Event Event Selector Selector dialog will appear Select the appropriate events E 28 Jan 1998 E 2 L 27Fe01998 gt sama aloras 2 a ul and click OK After each event is kriged you will be prompted to enter the ASCII grid file name To avoid check Overwrite Existing Files If this option 1s selected Ol roer the UI will generate and use default ASCII grid filenames AA Pg if 10 Sep 1998 and save them in the project directory The default file MEE repeating this step click on Tools Project Settings then name is constructed as project file name event date for example newproject 28 Jan 1998 asc All kriged grids will be added to the project map If you don t want your kriging grid files to be added to the map click Tools Project Settings and uncheck Add Results to Map It may be necessary to do this if you have a large number of kriging events because plotting each map can significantly slow down your system To generate contours in multi event projects select Plot Contours The Event Selector dialog will appear Next to the Event is the column GridFile populated with the default equivalent ASCII grid file name If the ASCII file
84. of the compiled FORTRAN and Visual Basic executa bles used in preparation of this report are available by contacting Matthew Tonkin at the address provided References Air Force Center for Environmental Excellence AFCEE 2000 Comprehensive long term monitoring plan version 1 0 August 2000 Prepared for AFCEE MMR Installation Restoration Program by Jacobs Engineering Group Inc Chiles J P and P Delfiner 1999 Geostatistics Modeling Spatial Uncertainty New York John Wiley and Sons Clark I and W V Harper 2000 Practical Geostatistics 2000 Columbus Ohio Ecosse North America Lic Delhomme J P 1978 Kriging in the hydrosciences Advances in Water Resources 1 no 5 252 266 Deutsch C V and A G Journel 1998 GSLIB Geostatistical Software Library and User s Guide 2nd edition New York Oxford University Press Ferris J G D B Knowles R H Brown and R W Stallman 1962 Theory of aquifer tests U S Geological Survey Water Supply Paper 1536 E Gaganis P and L Smith 2001 A bayesian approach to the quantifica tion of the effect of model error on the predictions of ground water models Water Resources Research 37 no 9 2309 2322 Hess K M S H Wolf and M A Celia 1992 Large scale natural gradi ent tracer test in sand and gravel Cape Cod Massachusetts 3 Hydraulic conductivity variability and calculated macrodispersivi ties Water Resources Research 28 no 8 2011 2027 Rouse H ed 1949
85. ols dll exists in MapWindow l Archive Project Tool plugins folder usually CSV to Shapefile Converter Document Launcher C ProgramFiles MapWindow Plugins or GIS Tools C ProgramFilesVWMap Window Plugins KT3D H20 O KT3D H20 A The KT3D H20 button should now appear on your MapWindow Menu bar Click on this button to open the KT3D_H20 User Interface UI Watershed Delineation Main Menu Main Toolbar Tab Selector KT3D P20 OTT_2007 Imported Data has 8 Header row No Header Row X StPIn83 ft Y_StPin83 1 water lev sys loc_ tf ratero eszasaos eses um o glans s rs Joso hr input Data File ARANA 4 2 12621833 98 662143 83 636 75 w 102 alerce exes ez fra 619 67 W 121s mass 9 2 12621768 97 659975 49 61861 W 121 niaan aner for un gje enes foe for E LU gt Data Table Creating a new project In order to use KT3D H2O you first need to create a new project or open an existing one There are two types of projects that can be used for the kriging the Single Event type for the kriging one data set and Multi Event type for kriging multiple data sets The Single event type 1s used to create a single result for example a single map of overall average water elevation The Multi Event type is used to create multiple results corresponding to multiple events for example this type would be used to create several maps each showing water levels from a different sa
86. one indicating the locations black circles from which a parti cle released will be captured by the recovery well Gray crosses indicate particles that leave through a domain boundary Order data must be written for Surfer grid fille 11 12 13 13 15 15 16 17 17 18 Outline This document describes a program Transient Iracker for calculating approximate travel paths Transient lracker requires as input at least one grid of hydraulic head This grid can be generated by any number of methods including interpolation of observations analytical solutions and numerical simulation results Use of the program should be accompanied by review of the references and dis claimer provided at the end of this Documentation and Verification Package Transient Tracker is programmed in Fortran 90 95 using a modular program struc ture TransientIracker has been developed to be independent of any specific model platform requiring simple ASCII input files and producing ASCII output files The programs can be obtained free of charge together with an example data set by writ ing to mattQ sspa com The performance of TransientTracker has been tested in a variety of applications Future applications however might reveal errors that were not detected in the test simulations Users are requested to notify matt sspa com of any errors found in this document or the programs 1 Transient Track
87. options for the calculated grids Selected Output Format Grid Format Particle Line Format ASCII Surfer v7 Grid S e ArcMAP ESRI Shape SHP file Times associated with pathlines are written in units that correspond with the specified hydraulic conductivity units in the GUI s Part Track tab 2 All methods result in the production of the file CAPTURE OUT 3 Appendix C describes the ASC grid format Disclaimer This software and documentation is provided AS IS without warranty of any kind including without limitation the warranties of merchantability fitness for a particular purpose and non infringement The entire risk and responsibility as to the quality and performance of the Software is borne by the user The author s disclaim all other warranties The following text from the GSLIB KT3D program details the copyright and distribution rights pertaining to the GSLIB programs Copyright C 1996 The Board of Trustees of the Leland Stanford Junior University All rights reserved The programs in GSLIB are distributed in the hope that they will be useful but WITHOUT ANY WARRANTY No author or distributor accepts responsibility to anyone for the consequences of using them or for whether they serve any particular purpose or work at all unless he says so in writing Everyone is granted permission to copy modify and redistribute the programs in GSLIB but only under the condition that this notice and the
88. ordinate of grid zmin zmax minimum data value maximum data value data for every node the surface data value listed in the order presented in Figure 14 Data is written in order from lower left to upper right row 1 col 1 to row NROW col NCOL If there are 10 rows and 10 columns 100 data values must be listed Row NROW Row 3 G Row 2 2 Row 1 O Col 1 Col NCOL Figure 14 Order data must be written for Surfer grid file
89. outside the convex data domain For purposes of this study the maps used for the particle tracking exercise mentioned were created in a single kriging step using a default linear semivariogram however the authors suggest that appropriate semivariogram selection and fitting should be con ducted as part of any rigorous study of ground water level data Jackknife Model Comparison The uncertainty related to kriging approaches or models is often assessed by mapping the kriging standard deviations and or the Lagrange multipliers These are intimately related to the mod eled semivariogram parameters i e the sill nugget and range and are not directly influenced by the form of drift model used The form of the kriging equation Equation 1 can be considered as two stacked models i e the expression representing the drift term and an expression or series of nested expressions representing the residual semivariogram The linear log drift approach represents a revision of the drift term m uJ and does not directly affect the methodologies for modeling of the residual R u component which in either the linear log or linear case is modeled as a single or series of stacked analytical approximations to the calculated semivariogram Ideally of course if a better drift model is used the calculated residuals may be smaller resulting in a smaller vari ance and smaller kriging standard deviations However semivar 10gram modeling c
90. ping of up to n extraction or injection wells can be summed Le Sy Z yo In r 6 Where s is the drawdown at location i P L Q is the pumping rate at the nth extraction well LAT r is the radial distance of extraction well Q from location i JX L and i J may represent row column grid location or Cartesian coordinates The complete linear log drift is then invoked in the kriging rou tine as Drift A BX CY s 7 By including the logarithmic component the drift model approximates the principal physical processes that govern ground sy Oe GS 10 Plume De ih 7 l 4 o Y 7 b Kon 1000 2000m Figure 1 Location of CS 10 piume Massachusetts Military Reservation Cape Cod Figure 2 Location of monitoring and extraction wells of the CS 10 plume and the local area of well capture estimation ae ee ee AAN water flow and ultimately govern the autocorrelation of ground water elevation data Accordingly assumptions underlying the Theis equation are implicit in the kriging routine principally Rouse 1949 e The pumping well penetrates and receives water from the entire saturated thickness of the aquifer e The aquifer is confined if the aquifer is unconfined drawdowns should be less than 10 of the saturated thickness of the aquifer e The aquifer is homogeneous isotropic and of infinite areal extent e The drawdown and or mounding has reached a st
91. racters long xSize ncol 1 One dimensional array representing spacing between adjacent nodes in the X direction between columns LL yLL double Y coordinate of the lower left corner of the grid Txt One dimensional array representing spacing between adjacent nodes in the Y direction between rows 33 For each grid data in grid array section binary file contains EventDate Long Event date in format of number o days counted from 1900 Grid nLay nRow nCol Double Grid Array The grid values are stored in row major order starting with the maximum coordinate The first grid value in the grid file corresponds to the upper left corner of the map The second grid value is the next adjacent grid node in the same row the same Y coordinate but the next higher X coordinate 34 Appendix C ArcInfo ASCII Grid Files Formats ArcInfo ASCII Grid files asc contain seven header lines that provide information about the size and limits of the grid followed by a list of Z values The fields within ASCII grid files must be space delimited The listing of Z values follows the header information in the file The Z values are stored in row major order starting with the maximum Y coordinate The first Z value in the grid file corresponds to the upper left corner of the map The second Z value is the next adjacent grid node in the same row the same Y coordinate but the next higher X coordinate When the maximum X value is reached in t
92. rdinate second as Y coordinate third as kriging variable and fourth as an object name Any input option column reference can be changed using the drop down menus For multi event projects a fifth variable Event 1s required in format of Julian date for example 01 01 2004 Well drift data Data defining locations and characteristics of each well used as a well drift should be provided in following format Variables 1 Header Line 2 qaxx i qyyi qqq i idtwell i qdrift i qtype i wellname i qevent i where this line is repeated nwells times The parameters listed above have the following definitions NWELLS KT3D H20 will read file to the end so no need to specify the number of wells Lines begin with character are considered as comment lines qxx i X coordinate of the well i qyy i Y coordinate of the well i qqq i Pumping rate of the well i for the current event wellname i A name for the well gdrift i Drift term for well i qtype i Specify the well as recovery R or not recovery N Used in capture zone analysis gevent i Event Date in format of Julian date Line Drift Data LINEFILES 1 These files define the locations and characteristics of sink line segments They are simple ASCII files and provide information in the following format 31 Variables l Header Line 2 lxs i lys i lind i lval i where this line is repeated NLIN times The parameters listed above have t
93. rid file asc and click Open 18 checkbox then from File open dialog select Kriging binary file The UI will read all saved events in the binary file the Event selector dialog will appear Select which events to plot This will generate new ACII grid files for each selected event You will be prompted to enter a file name for each To skip this step before importing the binary file click on Tools Project Settings in the main KT3D H20 window then check Overwrite Existing Files If this option has been selected when the binary file is imported the UI will generate and use default ASCII grid filenames for each event and save them in the project directory The default file name is constructed as project file name event date for example newproject 28 Jan 1998 asc 19 Append new Events To append a new sampling event s to an existing Project data set click Tools gt Append Data then select the appropriate dataset to append In the dialog form select appropriate columns as explained in the Importing Data section To confirm that your new data set is imported correctly click OK The new data will be appended to the end of the data table Generate Contours Convert Excel to Shape Composite Target one Append Data variable Deja Set Combine Binary Files Well Drift Data Sek Project Settings view Run ETSO Log 20 Particle tracking The grids generate
94. rift Model Monitoring Well Injection Well Extraction Well Figure 1 Plan View Comparison of Water Levels Kriged Excluding and Including Pumping Well Drift Term Regional Gradient Known Linear Drift Profile Linear log Drift Profile Figure 2 Section View of Water Levels from Above Kriging Example GSLIB GSLIB is an acronym for Geostatistical Software LIBrary referring to a collection of geo statistical programs developed at Stanford University One of these programs is KT3D a general program for point or block kriging in two or three dimensions The GSLIB programs are fully described in Deutsch and Journel 1998 KT3D H20 is based upon KT3D It is strongly recommended that users of the KT3D H20 programs obtain a copy of Deutsch and Journel 1998 both for the theoretical discussions of geo statistics provided therein and for the detailed descriptions of the input files required and output files produced by the KT3D program Details of these input and output files are not provided in this documentation However the section KT3D H20 Program Inputs described additional inputs that are required beyond the standard KT3D inputs In particular KT3D uses an integer array IDRF to indicate which drifts are to be included in the kriging The standard KT3D IDRF array includes nine integers for the nine drifts available The additional drifts added to KT3D H20 are implemented by extending this IDRF array to include prese
95. rticle tracking parameters The following parameters are required to perform particle tracking Input type format Hydraulic Conductivity in Aquifer Entered as single numeric value in GUI Porosity in Aquifer Entered as single numeric value in GUI May be specified in using GUI as described or imported from an external file Supported file types Starting locations of particles Microsoft Excel or ASCII text including XY coordinates of each starting location or an ESRI shapefile shp showing all starting locations asc files generated by KT3D When KT3D is run Results of KT3D water level these files are saved automatically in the same kriging directory as the xpar or xpars file and are imported automatically before particle tracking is run For practical reasons all input parameters which contain a time component must use the unit days 21 For explanation particle tracking parameters please refer to the included Transient Tracker documentation Attachment 2 Setting particle starting locations There are five options to generate particle starting locations Custom Regular Grid a Read from File To import starting locations from a file under the Part Tab click IS button to expand the KT3D H20 main window Then click Open file button next to Start Loc File xccod EIN Y coord REN v Select the type of input file ASCII Excel or Shapefile After data are import
96. s 14 Model Variogram Type of Semivar Model fit p Spherica Sill Variance Contribution c Nudget Constant c0 pometric Anisotropy Max Horizontal Range a_hmax Min Horizontal Range a_hmin 1579 Angles Defining Geometric Anisotropy Azimuth Correction A Horizontal Anisotropy 19 amp Semivariogram Event 1 U 28Jan 1998 Sellect All 23 Mar 1998 e Je orageraso sledene Variance Contibution Experimental Varigram Curves E 2000 Appl Lance Lag Distance After adjusting model parameters it is necessary to click on Apply button to recalculate model using GSLIB vmodel program and refresh the plot At any time you can switch to the experimental page and adjust experimental parameters After parameters are adjusted click on Apply to execute gamv program and refresh the variogram plot Modeled Variogram Experimental Variogram Dip angle Dip angle tolerance Dip bandwidth Semivariogram Lag Distance 10 3 After the appropriate parameters are entered and best fit is achieved click the OK button to return to variogram page 15 Running the Kriging Before kriging it is recommended that you save your MapWindow project file and your n KT3D parameter file To execute the KT3D kriging program click the bat button Y ou can terminate kriging at any time by pressing the ESC key Single even
97. s added to account for the potentiometric response of a water table unconfined aquifer to infiltration through the base of a circular pond The approach is based on the Analytic Element Method AEM described by Strack 1989 For a circular pond of radius R this can be represented by the following schematic and equations A ca iia A so EEE Within the element 1 0 lt r lt R Gy Ca YX Y R la y RE 8 Outside the element 2 2 2 R lt r lt G x yxp yp R BAS HHT 9 R This essential information can be distilled and combined with the linear logarithmic and line sink source drifts shown in 7 to give H x y A BX CY D Qilogio ri Ed LG F2 P r e x y 10 1 Where P r mounding factor due to effects of the leaking pond feature F the linear regression coefficient for the leaking pond features p the summation from 1 to o where o the number of pond features 1 This drift is only compatible with 2 D kriging This drift can be used in combination with the Point Sink or Source of Known Strength and with the Horizontal Line Sink or Source of Known Strength and with any of the standard drifts included with KT3D KT3D_H20 Program Inputs This section describes the names and values of variables required in the modified KT3D PAR file and the names and formats of new input files that are required to implement the hydrologic drift terms and or the par
98. sed For the Cape Cod dataset the most visually appealing results are achieved using a short range linear or spherical semivariogram to describe the near field variance Maps of grids created with default horizontal i e the drift linear and spherical residual semivariograms are presented for comparison Figure 14 The linear and spherical model semivariogram maps are quite similar in appearance which is probably because the spherical semivari c Linear Log 1000 m Figure 14 Water level contours constructed with a horizontal b linear and c spherical semivariograms in addition to the hnear log drift M J Tonkin S F Larson GROUND WATER 40 no 2 185 193 191 om y rA p D 3 v Measured Meters msh O Linear log Model Linear Mode Figure 15 Measured versus modeled water level from the jackknif ing analysis ogram is linear at low lag distances The commonly cited log nor mal approximation for the distribution of many hydrogeologic properties such as hydraulic conductivity Roth 1998 might sug gest an exponential semivariogram is also an appropriate selection However experimentation with a number of different water level datasets kriged using the linear log drift model and various resid ual semivariograms suggests that typically linear and spherical semivariograms produce maps that describe the data satisfactorily and quickly return to the drift
99. starting location and the simulated dispersion By starting all 100 particles at a single point Figure 12 provides a comparison to Figure 11 and demonstrates that the simulated dispersion as opposed to initial particle location is the dominant source of spreading as the particles progress towards the well The advection only particle track originating from the single point source is provided in the background gray for reference For remediation purposes it is often helpful to assess the capture region for a given scenario The capture out file was used to identify locations where particles released at the beginning of the simulation would get captured by the well The red dots in Figure 13 indicate the locations that will be captured by the well while the blue crosses indicate locations where particles move out of the domain instead of being 17 Figure 10 Transient Tracker particle paths with longitudinal 2 5 feet and transverse 0 5 feet dispersion Figure 11 Particle locations black at 8688 7 days 18 source at 401 H tritt t tt from a point HEHE EEE EEE EE EEE EEE EE EEE EEE HEHE HEHEHE He Hee et HEE EE EEE EEE HEHEHE HEHEHE HEH eee e sd ls ds dl e eee beh ee tee test PEE tet 44444444 tett tt tt PEPE AAA AAA Ae
100. t kriging To run kriging click the LEN button After kriging is finished the UI will prompt you to enter an ASCII grid file name The grid will be saved in the same directory as the par or xpars file and imported to the MapWindow project map MapWindow automatically generates a bmp file for viewing purposes and an mwleg file which is XML file that contains layer legend information KT3D_H20 also generates an XML file xasc which contains all parameters and all input data used for the kriging Data from XML file can be imported at any time selecting the File Import Xml Data To generate contours select Plot then Contours A file selection dialog will appear Generate Contours Select the appropriate grid file and click OK Use contour interval The Generate Contours dialog will appear Calculated Range Min Value Interval Max Value Contours levels may be set two ways Fist you may set the maximum and minimum values and NENNE contour interval By default the maximum and 610 615 620 625 639 minimum contour values are determined from the HTA grid but these values may also be entered EEE 999 entering level values separated by a single space in the text box After you have manually Second you may specify levels by determined the contour levels click the Generate button This will generate a shapefile shp showing the contours You will be prompted for the shapefile name and the l
101. t used maximum search radii angles for search ellipsoid 0 SK 1 OK 2 non st SK 3 exdrift drift X y Z XX YY ZZ XY XZ ZY Q L PP 0 variable 1 estimate trend gridded file with drift mean column number in gridded file 1 0 0 nst nugget effect 1 1 0 0 0 0 0 0 0 it cc ang1 ang2 ang3 20000 0 20000 0 20 0 a_hmax a_hmin vert 1 500 100 0 2 1 0 8 50 1 5 tracking iback nptp hydcond porosity stepsize nparticles xprad nrads nout l e 4 1 e 10 0 80 1 e 6 1 e 3 roerr tiny safety eps vsmall note the code knows if particle tracking has been selected by an integer flag passed from the VB GUI to the KT3D_H20 DLL 5 858951 242823 43316 R 859806 239179 43315 R 857654 241948 52941 R 859752 241291 43316 R 860383 240985 48128 R Horizontal Line Sink or Source of Known Strength The KT3D_H20 suite of programs is supplied together with an example multiple line sink source data set and output files in Surfer format Verification 2DSink srf showing the resulting water level surface and example particle tracks This example data set includes two line sinks this example data set provided with the program The first Figure 5 2D Sink of Known Strength i Sinks i MODFLOW iii Ordinary Kriging no Sink Drift iv 2D Sink Drift Blue mon
102. ted Deutsch and Joumel 1998 The Theis equation for drawdown in response to pumping can be approximated using Ferris et al 1962 Rouse 1949 Q 2 25Tt AT nl S 6 where Q pumping rate at extraction well L3T S aquifer storage T aquifer transmissivity L T s drawdown of the potentiometric surface L r radial distance to the pumping well L t time since pumping began T m 3 14159 In natural logarithm Equation 3 describes a logarithmic cone of depression centered on the extraction well This can be rewritten as s n 2220 2 Merg 2n 4 At any time when the change in hydraulic gradients 1s zero the first term in Equation 4 can be considered a constant and the 186 MJ Tonkin S P Larson GROUND WATER 40 no 2 185 193 E drawdown at a monitoring well is inversely proportional to the log arithm of the radial distance of the monitoring well from the extrac tion well proportional to the pumping rate Q and inversely pro portional to the transmissivity T Combining Equations 2 and 4 the drift termed linear log in the following discussion is described by Q Drift A BX CY AT In r 5 Because the transmissivity is assumed constant throughout the aquifer the relative magnitude of drawdown at a monitoring well due to pumping at multiple extraction wells is determined only by Q and r Using the principle of superposition the drawdown due to pum
103. ther gridding software applications e Point Sink or Source of Known Strength accounts for mounding or drawdown in response to injection or extraction at a known rate at one or more wells e Horizontal Line Sink or Source of Known Strength account for mounding or drawdown in response to horizontal linear features of known extraction injection rate such as interception trenches or infiltration galleries and e Circular Leaking Pond of Known Strength accounts for the potentiometric response of a water table unconfined aquifer to infiltration through the base of a circular pond The available drift terms can be applied simultaneously 1 e a single gridded surface may contain point sinks or sources horizontal line sink or circular leaking pond In addition in order to account for heterogeneity different groupings of the drift elements are possible so that scaling provided by universal kriging is performed independently on each group to obtain a best fit e g wells located in a high transmissivity zone can be assigned to Point Sink Drift Term 1 and wells located in a low transmissivity zone are placed in Point Sink Drift Term 2 These gridded surfaces can be used to complete the following types of hydrogeologic analyses maps for single or multiple events maps of water level elevations maps showing particle traces particle tracking and e maps of particle capture capture zone analysis including capture frequency maps
104. ti 1978 This universal krig ing approach is not typically adopted for gridding ground water level data Despite the extensive literature that discusses kriging calcu lating custom drift functions is not a straightforward matter and stan dard approaches rarely extend beyond linear and polynomial drift models Chiles and Delfiner 1999 In areas of fairly uniform regional hydraulic gradients the linear drift can improve the aes thetics of a contour map However visual Inspection of contours gen erated in this manner indicates that the linear drift does not produce a surface that is adequately close to conserving flow in areas of local ized discharge or recharge S S Papadopulos and Associates Inc 7944 Wisconsin Ave Bethesda MD 20814 301 718 8900 fax 301 718 8909 Matt SSPA com SPL SSPA com Received April 2001 accepted November 2001 DT TATION WATT e A AIAN E As a consequence interpretation of water levels constructed without a drift model or using a linear drift is typically limited to broad features such as principal direction s of flow and areas of significant drawdown or mounding Although this capability can be improved by increasing the number and density of monitoring wells provided the wells are suitably located water level mon itoring budgets rarely allow for a network sufficient for accurately representing the curvature of the potentiometric surface near extrac tion wells Such a network is particu
105. ticle tracking described above First the variables that are required within the modified KT3D PAR file are listed and described New PAR File Variables All additional inputs required beyond those usually supplied for kriging water level data using KT3D are now detailed The following entries in the PAR file for kriging with new drift terms must be placed at the END of the 9 typical drift integers 1drif 10 idrif 11 The following entries in the PAR file for particle tracking must be placed together on one additional line at the END of the KT3D PAR file These variables are only read if the particle tracking option is selected on the GUI KT3D H20 iback nptp conduct porosity stepsize nparticles xprad nrads nout If idrif 10 O or is absent no action is taken idrif 10 If idrif 10 1 the 2 D linear log drift term is added KT3D H20 expects to find a file SDWELL DAT in the working directory that lists the extraction and or injection wells Extraction is indicated by a positive rate If idrif 11 0 or is absent no action is taken idrif 1 1 If idrif 11 1 the 2 D line sink drift term is added KT3D H20 expects to find a file 2DSINK DAT in the working directory that lists the sinks sources Extraction is indicated by a positive pumping rate Iback If iback gt 0 perform backward tracking If iback lt 0 perform forward tracking The number of particle tracking steps to take
106. trictly compatible only with 2 D kriging and can be used with any of the standard drifts included with KT3D To include the 2D well function drift click on the check box labeled 2D Well function Q2D If well drift data have not been imported previously a file selector dialog will open Supported input file formats Microsoft Excel xls xlsx Xlsb and xlsm files Microsoft Access mdb and accdb files ESRI ShapeFiles shp and ASCII txt or dat 11 Navigate to the appropriate input file and click OK This will import the well drift data into KT3D H20 and open the 2D Well Drift dialog To view your original data or to select a different input file click Show data at the bottom right of the dialog window 2D Well Drift X Coord Y Coord Well Name Drift Term Recovery Le penca lees le lev a a a O Headerron No Header Row gt izcziscaos fesos 7 ew7 1 ee fonemer sov Corova E Mize ce Joson o ews v TT EE fore ai EE EZ 262320957 esos fes fewa 1 faens ES gt TE fas CTE v E gt AECI CC CA CTI v fnise oss Jest fm ens fer gt EE feam a rr By default X and Y coordinates are the first and second columns in your input data set pumping rate is the fourth column well name is the fifth and drift term in sixth This can be changed by selecting the appropriate columns using drop down menus under each of data table columns Selecting the value None in the dri
107. ture immediately apparent This result is expected because estimation of the trend sur face assumes the residuals to be uncorrelated At first glance a dilemma may appear unavoidable when selecting a suitable semi variogram model however residuals can be expected to show local correlation The calculated semivariogram for the residuals from the linear log drift is presented as Figure 13 together with an example spherical model bin width 150 m This semivari ogram plot spans the entire dataset and was constructed using equi width bins such that the number of point pairs i e weight or support representing each plotted point varies greatly Plotted val ues for separation distances greater than 1650 m are supported by fewer than 15 point pairs in particular the last two are each sup ported by only one point pair Beyond this distance the combined impact of lack of support and boundary effects render the semi variogram untenable This supports the conclusion that the covari ance Is typically not well known or estimatable beyond one half the field size Deutsch and Journel 1998 and hence that the best results should be achieved using a semivariogram addressing only half the field size and a search radius of one quarter the field size For the Cape Cod dataset wells to the southeast may be affected by ground water extraction activities several thousand meters to the southwest that are not explicitly included in the drift model u
108. us water level Cape Cod dataset In profile the calculated surfaces differ markedly Figure 9 The surface generated from the linear dnft model is perhaps best described as muted In the area upgradient northeast of the extrac tion well and downgradient southwest of the injection well the slope diverges from the known uniform background gradient Alternatively the surface generated from the linear log model dis plays the characteristic cones of impression and depression around the injection and extraction well respectively at the margins of the gridded domain the slope is converging asymptotically logarith mically on the uniform background gradient Because the combined regional linear and point logarithmic drift specifically accounts for the drawdown and mounding distribution of the residual error throughout the domain does not significantly affect the calculated background hydraulic gradient The coefficients of the fitted linear drift surface Equations 7 and 8 are 100 88 A 0 00045 B and 0 00043 C m respectively here the gradient coefficients B and C are 50 of the known gradient coefficients Residual Error and Semivariogram Selection Sources of residual error fall into two broad categories mea surement error and model error which includes deviations of the test data from model assumptions This paper does not include a rigorous investigation of error because the primary intention is to p g v
109. vels the assumed measurement errors and the linear log drift gridding approach employed a particle originating from the given location would be captured by the combined pumping of extraction wells about 50 percent of the time Hence these maps illustrate the relative frequency with which particles of groundwater are captured under the varying conditions represented by different water level events A capture frequency map may be generated two ways First it will be generated automatically at the end of a capture zone analysis After tracking has been completed for all events a prompt will appear asking if you want to save the capture frequency map Specify the path and file name and click Save Second a capture frequency map may be created from the combination of any capture grid files Select Plot Frequency Map then select desired capture zone analysis gridfiles Specify the path and file name and click Save The capture frequency map will be automatically added to the MapWindow project map Exporting Hydraulic Capture Zone analysis results Capture Zone analysis results can be exported and saved as a binary file cbf for file format see Appendix B To do that select File Export KT3D H20 Binary file Then in file type dropdown menu select KT3D H20 Capture Binary File cbf Enter the file name For Multi Event projects the in the Event Selector dialog box will appear Select the event capture grid files you

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