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Geostatistics for Waste Management: A User`s Manual for the

1. 17 DATA DSTAT GEOEAS and PROG These menus are for respectively available data sets default statistics program GEO EAS geostatistical software and user defined programs Additional menus and programs can be added by following the instruc tions on modifying the USER MENU given in Section 2 5 2s iO Description of the View Feature F4 If for some reason you are located at one of the menus and you need to see the last screen of output from a program that has just been completed you can toggle between the menu screen and the program screen by typing F4 provided your monitor and graphics card allows multiple screens 2 5 e Description of the USER Menu F5 Thu Jun 29 1989 07 47 45 am Return to Main Menu ISTICAL PROGRAMS Main Menu Quit GEOPACK Data Set Utilities Menu Statistics Menu Variogram Menu Ordinary Co Kriging Menu Disjunctive Co Kriging Menu User Menu Return To Main Menu EPA GEO EAS Graphics Menu Statistics Package Default Data Base Management Default User Programs F5 user menu If the F5 key is pressed from any menu the USER s Menu is activated The USER s Menu allows GEOPACK to be modified to include other programs and menus which are defined by the user The instructions which tell GEOPACK which program to run or menu to display are in a fi
2. An alternative method for saving the output from the semivariogram program is to save the output from only those runs that produce reasonable results This can be done by selecting OPTION KEY S at the end of the Sample Variogram Calculation program The OPTION KEYS appear at the lower right hand corner of the screen during execution of a program The S option only appears at or near the end of the program and generally after a graphic plot of the sample semivariogram has been produced Fit Model Automatically To Sample Variogram This program allows you to fit a mathematical model e g a gaussian exponential linear spherical or power model to a sample semivariogram The fitting method uses the nonlinear least squares minimization technique of Marquardt 1963 Sample Autocorrelation Functions Saved MOIST MOIST 00 01 02 03 04 MOIST TEMP 00 O1 MOIST SAND TEMP TEMP 00 TEMP SAND SAND SAND 28 To specify a sample semivariogram first step in running this program a screen is produced which shows all the saved variograms for each random function and all the cross variograms for each pair of random functions This screen displays the random function name M M OIST MOIST OIST TEMP TEMP followed by a series of numbers such as MOIST M MOIST OIST TEMP 00 03 The numbers indica
3. GEOPACK requires that a cutoff value be supplied during execution of the programs The cutoff value is used to indicate missing data The cutoff value is a specified value that is larger than any of the true data in the data set For example if you have a variable that is missing a value at a point in space in the data set you place a value which is larger than any of the true data and larger than the cutoff value which you must specify During execution of a program you will give a value called the cutoff value which is used by the program to determine which values to ignore Any value in the data set that is greater than the cutoff value will be ignored by the program It is imperative that the cutoff value you specify is appropriate for given data set if not the resulting calculations will be inaccurate 21 For example given the following data index X y variable 1 variable 2 variable 3 3 10 0 11 2 12 55 45 66 1002 321 15 14 9 1 9 11 83 48 19 1032 209 5 18 7 7 7 12 91 36 98 1200 500 7 3 2 14 5 9 50 9999 99 1002 321 45 46 4 16 4 16 82 45 66 1002 321 the value used to indicate missing data is 9999 99 Note that this value is greater than any value of ALL the variables An appropriate cutoff value to input into GEOPACK would be greater than 2000 since 1200 5 is the largest true data value Modify an Existing Data Set This program allows the creation of new variables in an existing data set
4. tells the menu program to add a menu to the screen wher the name following is the file containing the menu instructions Pop the menu on the screen tells the menu program to remove the top most menu from the screen Sometimes the remove menu instruction i e is given on two consecutive lines This is done so that two quit menu key strokes are not needed to return to the proceeding menu this is only done when an additional copy of the User s Menu is popped on the screen to move it 38 side which is done to improve visual appeal menu off the screen the menu option If there are two or more entered STEP 3 If Another MENU Is Being Added from the right hand side of the screen to the left hand Ves Push the the underscore before the G on line 2 is used to designate the highlighted character This character will activate menu options with the same highlighted character the cursor bar will move to the next one ach time the highlighted character is It is often best to place the new program into a separate subdirectory An example of this is the GEO EAS subdirectory which stores th for the GEO EAS geostatistical software system Once the and created the newly developed program s and auxiliary f into it A new data file containing the entries for the ne e executable programs subdirectory is named iles should be copied w
5. r than including all these commands nited to h The second step is to alter US R MEN to 1 entries on any one menu include another or alter an existing heading Once the program or menu to be added to GEOPACK has been created it can be accessed through the USER menu i e F5 key by adding or modifying an entry to the menu file Entries to the USER menu are added by editing the USER MEN file located in the root of the geostatistical programs i e GEODIR USER MEN An example of a menu entry is Line 1s SlE User Menu 23 _GEO EAS 3 message 4 i Be S GEODIR user men 6 COMSPECS c cd GEODIR user geoeas 7 ai 8 SGEODIR user geoeas GEOEAS MEN where the symbols have th in column indicate th and the col for exampl 0 Black 1 Blue 2 Green e Menu colors are the background and foreground colors lors are given by the col e a dark blue background lettering is specified by using S lI e following meaning 8 9 A 37 indicates that the next two hexadecimal numbers where the first and second numbers respectively lor numbers given below with light yellow in line 1 above i h B Grey Light Blue Light Green 3 Cyan B Light Cyan 4 Red c Light Red 5 Magenta D Light Magenta 6 Brown E Light Yellow 7 White F Light White
6. EOPACK TMP EOPACK USER DATA TI MICROS1 GRAPH SURF MFOXPLUS Columns 1 10 20 This file is used by GEOPACK during operation of the programs At any time if there is a change in the definition of any item in SYSDEFLT a change needs to be made to this file The easiest way to do so is to use the Change System Default Settings option on the Utilities Menu i e F3 key 16 To manually run the Default Settings program type DEFLT sysetup sysdeflt from the root directory of GEOPACK This may be necessary if the sysdeflt file is ever accidentally deleted or modified DOS Shell This Utility allows you to temporarily exit the GEOPACK system and return to the MS DOS command line mode When you exit to a DOS shell the text color on the screen will be red This is to remind you that you are in a DOS shell Once you are finished running MS DOS commands you can return to GEOPACK by typing EXIT which exits you from the DOS Shell Please Note While in a DOS shell some of the available computer memory is still allocated to GEOPACK and if you try to run a program that requires a lot of memory you may s the message not enough memory If you must run this program you should exit the DOS shell i e return to GEOPACK then exit GEOPACK This will free up all the available computer memory Also it is possible to exit to a DOS shell and restart GEOPACK this can be done several times If
7. GEOPACK has been developed in cooperation with the U S EPA s R S Kerr Environmental Research Laboratory Ada OK It was developed with the philosophy that geostatistical software is needed that can be used as a learning tool by individuals with little or no geostatistical expertise and yet can also satisfy the needs of individuals with more advanced training in geostatistical methods The specific objectives in creating GEOPACK were to develop 1 geostatistical software which is easy to use so that those with little training in geostatistical methods can learn these techniques and eventually use them in their work environment 2 an integrated system which will free the user from excessive fil editing and program manipulation 3 a system which is adaptable in the sense that additional programs can be incorporated into the system by the end user at a later date without having to alter previous programs or recompile the entire system 4 programs which produce graphic output in a variety of forms and of publishable quality to meet the needs of research scientists and engineers and 4 software which includes on line help facilities and extensive error checking in the programs The on line help facilities offer information concerning the operation of the system its capabilities and limitations how to alter the system as well as programming conventions and definitions GEOPACK allows the incorporati
8. J M Disjunctive Kriging A Simplified Theory Math Gee 2306 321 1980 and R R Sokal Statistical Tables 2nd Ed W H Freeman and New York 219 pp 1981 A Geostatistical Approach to the Trickle Irrigation Design Heterogeneous Soil 1 Theory Water Resour Res 632 642 1983 A Geostatistical Approach to the Trickle Irrigation Design Heterogeneous Soil 2 A Field Test Water Resour Res 543 552 1984a Design of an Optimal Sampling Network for Estimating the Variogram Soil Sci Soc Am J 48 708 716 1984b F Statistical Analysis of Crop Yield Soil Water Relationships Heterogeneous Soil Under Trickle Irrigation Soil Sci Soc J 48 1402 1410 1984c A Geostatistical Approach to Solute Transport in Hetero geneous Fields and Its Applications to Salinity Management Water Resour Res 20 1260 1270 1984d 68 Russo D and E Bresler Soil Hydraulic Properties as Stochastic Processes I An Analysis of Field Spatial Variability Soil Sci Soc Am J 45 682 687 1981 Sisson J B and P J Wierenga Spatial Variability of Steady State Infiltration Rates as a Stochastic Process Soil Sci Soc Am J 45 699 704 1981 Sokal R R and F J Rohlf Biometry 2nd Ed W H Freeman and Co New York 859 pp 1981 Sullivan J Conditional recovery estimation through probability kriging Theory and practice Geostatistics for Natural Resources Characterization Part I G Verly et al Eds
9. In any other column the S is used for different purposes print the following text as the menu title print the following text as menu selection heading print following text in the information box at the top of the menu tells the menu program to hold the menu on the screen as long as possible before switching screens This helps to improve the visual appeal of the menu program but should only be used when popping i e adding or pushing i1 e deleting a menu and not when running an executable program It should be placed prior to the menu to be added or deleted indicates that the remainder of the line is to be executed THE MENU PROGRAM WILL ONLY RUN EXECUTABLE FILES AND NOT BATCH FILES OR BATCH COMMANDS To run a BATCH command the following method must be used COMSPECS c cls this will clear the screen SCOMSPECS c echo this will echo S COMSPEC S c cd c this will call the directory c The name of the file to b xecuted must be either in the current directory include a full path specification or the file must be in a directory on the DOS path It is generally a good idea to include the full path of every program whether you expect the program to be in the current directory or not since it may not be obvious what the current directory is You can always change the current directory using SCOMSPEC c CD lt new subdirectory gt
10. pp 365 384 1984 Task Committee on Geostatistical Techniques in Geohydrology American Society of Civil Engineers Review of geostatistics in geohydrology 1 Basic Concepts In Press American Society of Civil Engineers 1990 Task Committee on Geostatistical Techniques in Geohydrology American Society of Civil Engineers Review of geostatistics in geohydrology 2 Applications In Press American Society of Civil Engineers 1990 ten Berge H F M L Stroosnijder P A Burrough A K Bregt and M J de Heus Spatial Variability of Physical Soil Properties Influencing the Temperature of the Soil Surface Agric Water Manag 6 213 226 1983 Thomas G B Calculus and Analytical Geometry Addison Wesley Inc Reading Mass pp 1034 1972 Vauclin M S R Vieira R Bernard and J L Hatfield Spatial Variability of Surface Temperature Along two Transects of a Bare Soil Water Resour Res 18 1677 1686 1982 Vauclin M S R Vieira G Vachaud and D R Nielsen The Use of Cokriging With Limited Field Soil Observations Soil Sci Soc Amer J 47 175 184 1983 Vieira S R D R Nielsen and J W Biggar Spatial Variability of Field Measured Infiltration Rate Soil Sci Soc Am J 45 1040 1048 1981 Webster R and T M Burgess Optimal Interpolation and Isarithmic Map ping of Soil Properties III Changing Drift and Universal Kriging J Soil Sci 31 505 524 1980 Warrick A W D E
11. Figure 3 1 2 Example output from the Automatic Model Fit program The solid line is an spherical model that was fitted to the sample semivariogram 50 Line No No Pts 1 10 2 10 3 10 Variables TEMP TEMP TEMP DECAY DECAY TEMP DECAY DECAY ESC Exit Figure 351 233 DIR 00 00 00 SUMMARY OF SPATIAL CORRELATION MODELS MODEL EXPON SPHER POWER NUGGET 0165 L 2 33 0207 5 34 0000 00 Variogram Editor Model Nugget None None None Spherical A and the Edit Variogram Model File SILL NUGGET 0240 i 43 5 5 0197 4 98 0311 16 M RANGE SSQ 1 2286 00008 2 00 3 8252 00007 3332 21297 00016 lt 19 Model File G VIRUS VAR Sill Nugget 0 0 0 Home End Example output from Manual Model Fit in B 51 Select Model s Manual Mode program in Virus Decay Rate Meee o fon e es i S o n o o oOo om en O e oO O y Z nae hes 5 s wi ai n o mane Taa e N DS 4 x p i r i Distance kn Distance km Figure 3 1 4 Contour diagram of the estimated value of the decay rate using the Ordinary Co Kriging and Line Contour Diagram programs is illustrated 52 Estinate A Gata Vieu Estination Variance File KPLOT THP Of B 8 027926 6 832605 8 835405 8 0386
12. air and water systems Under a mandate of national environmental laws focused on air and water quality solid waste management and control of toxic substances pesticides noise and radiation the agency strives to formulate and implement actions which lead to a compatible balance between human activities and the ability of natural systems to support and nurture life The Robert S Kerr Environmental Research Laboratory is the Agency s center of expertise for investigation of the soil and subsurface environment Personnel at the laboratory are responsible for management of research programs to a determine the fate transport and transformation rates of pollutants in the soil the unsaturated zone and the saturated zones of the subsurface environment b define the processes to be used in characterizing the soil and subsurface environment as a receptor of pollutants c develop techniques for predicting the effect of pollutants on ground water soil and indigenous organisms d define and demonstrate the applicability and limitations of using natural processes indigenous to the soil and subsurface environment for the protection of this resource This user s manual serves the purpose of instructing the user in the use of GEOPACK a comprehensive user friendly geostatistical software system This guide should help th nd user both novice and sophisticated to become familiar with the features of GEOPACK By using GEOPACK and
13. 2 2 INSTALLING GEOPACK 2 2 a An in either a CGA rome or color monitor if it requires that properly Gl Installation Instructions installation of GEOPACK onto a hard disk 4 Mbytes o program can A INSTALL lt sourc or A INSTALL ESCRIPTION AND OP ERATION INSTRUCTIONS GEOPACK To completely f free space must be available on the hard disk be started by typing either A virtual disk can be used is defined to be the temporary storage the ANSI SYS driver be installed for the FOPACK requires hard disk storage of about EGA VGA or Hercules graphics adapter and the FOPACK has been written using a combination of Microsoft FORTRAN and C on IBM compatible microcomputers such as t S DOS operating system he ideally does not require a math Lo stallation program is supplied with GEOPACK to facilitate the install GEOPACK at least The installation drive gt lt destination drive and path gt If the optional lt source drive gt and lt destination drive and path gt are not specified the program will provide prompts for this information any legal floppy drive and the default value is A the hard drive path indicates geostatistical programs to specify a destinatio and subdirectory The default destination is C GEOPACK n drive and subdirectory since a number of programs are The for the The source drive can be destination drive and root of the
14. 2 5 h and 2 5 i i e variograms and kriging One difference between this program and the previous programs is that there are two screens of parameters that can be set for disjunctive kriging To toggle to the next screen type Ins Calculate Hermite Coefficients The first step in disjunctive kriging is the definition of a transform variable The transform variable is assumed to be hi variate normally dis tributed The program calculates the transformed values of the data set which are 35 used in the disjunctive co kriging program For each random function that will be used for kriging a transformed data set must be calculated i e run this program for each data set selected As a check on the transform process a comparison between the mean and variance of the data and the transformation is given and should be approximately the same Calculate Estimates The program GEODK is used to disjunctive kriging and cokriging The disjunctive kriging program allows up to 10 variables to be used for cokriging Up to 10 cutoff values can be specified for which the program will calculate the conditional probability that the estimated value is greater than the cutoff level During execution the output to the screen will use as heading designators the letters A through J Typing the F10 key will bring up a window that gives the definitions of the headings in terms of the cutoff values and transformed cutoff values Line and Block Co
15. Before making any modifications see Section Zoe s 2 3 SYSTEM OVERVIEW 2 3 a Program Structure The initial program structure of GEOPACK is shown graphically as GEOPACK DKRG KRIG STAT TMP USER DATA DSTAT GEOEAS UPROG VARI where in the abov xample the subdirectory GEOPACK is called the root of geostatistical programs The location of the root directory is specified during installation and can be located on any fixed disk drive and can be anywhere along a subdirectory tree It is recommended that the root be the first level subdirectory on a given drive The subdirectories DKRG KRIG STAT USER and VARI respectively are used to store the programs for disjunctive kriging and cokriging DRKG ordinary kriging and cokriging KRIG basic statistics STAT user defined programs USER and variography VARI The menu entries for each set of analyses except for the USER menu cannot be modified by th nd user The TMP subdirectory is created to be used as the temporary storage directory during installation The subdirectories of the USER directory DATA DSTAT GEOEAS and UPROG are examples of how GEOPACK can be altered to include additional programs The menu entries for the USER directory and its subdirectories can be modified by the end user to tailor GEOPACK for an individual s needs The instructions required to modify the GEOPACK USER m
16. Science Society of America Journal 52 1554 1558 1988 Yates Marylynn V and S R Yates Septic tank setback distances A way to minimize virus contamination of drinking water Ground Water 27 202 208 1988 Yost R S G Uehara and R L Fox Geostatistical Analysis of Soil Chemical Properties of Large Land Areas I Semi variograms Soil Sci Soc Am J 46 1028 1032 1981a Yost R S G Uehara and R L Fox Geostatistical Analysis of Soil Chemical Properties of Large Land Areas II Kriging Soil Sci Soc Am J 46 1033 1037 1981b Zirschky J Geostatistics for Environmental Monitoring and Survey Design Environ International 11 515 524 1985 Zirschky J and D J Harris Geostatistical Analysis of Hazardous Waste Site Data J Environ Eng 112 770 784 1986 Zirschky J G P Keary R O Gilbert and E J Middlebrooks Spatial Estimation of Hazardous Waste Site Data J Environ Eng 111 777 789 1985 70 u s GOVERNMENT PRINTING OFFICE 1992 648 003 60057 United States Environmental Protection Agency Center for Environmental Research information Cincinnati OH 45268 Official Business Penalty for Private Use 300
17. TEXT in the spawning process i e the abov command is equivalent to lt prog name gt g 1 11 provided that the system is setup so that the temporary directory is g and the border and text colors are 1 and 11 respectively The list of parameters EVOKE EXE can pass follows EDITOR Default text editor EMPDIR Temporary directory PRINTER Printer device PLOTTER Plotter device ROWS Maximum number of rows on screen COLS Maximum number of rows on printed page TEXT Text color BORD Border color MODE Screen mode 0 mono l color This only works in FORTRAN programs 41 SDATA EXE PACK EXE UNPACK EXE EXTRACT EXE EDIT EXE LISTDIR EXE DSTAT Default statistics package LGRAPH Default line graph package GRAPH Default contour 3 D graphics pkg DBASE Default data base management system Examples Try these examples in the root of the geos tatistical programs EVOKE defgraf LGRAPH TEMPDIR BORD TEXT EVOKE defgraf GRAPH TEMPDIR BORD TEXT EVOKE DBASE EVOKE DOSSHELL BORD S TEXT EVOKE SDATA TEMPDIR BORD TEXT EVOKE EDITOR EVOKE edit S EDITOR lt dir name gt BORD TEXT This program allows you to declare a data file active by copying it to the temporary directory e g RAM driv
18. calculated Shown in Fig 3 3 3 is a block contour diagram of the cokriging estimates and definition of the color pattern used in the diagram For this example a maximum of 5 nearest neighbors of the moisture and temperature within a radius of 20 m from the estimation site was used in the estimation process Shown in Figure 3 3 4 is the associated estimation variance for the soil moisture using the cokriging technique 61 Soil Hoisture Senivariogran 12 4 48 68 Soil Tenperature Senivartogran j 12 24 43 68 Distance a Figure 3 3 1 The semivariogram function for the surface moisture content in A and the surface soil temperature in B using the Variogram Calculation Sample program and the data see C912 DAT 62 Soil Hoisture and Tenperature Cross Senivariogran g 12 u J 48 68 Distance 1 Figure 3 3 2 The cross semivariogram function for the surface moisture content and the surface soil temperature using the Variogram Calculation Sample program and the data set C912 DAT 63 Cc we lt bas ee OO u OF On Aa UO M FigGube 333 3 Contour diagram of the estimated value of the electrical conductivity using the Ordinary Co Kriging and Block Contour Diagram programs 64 T OO File Data View Estimation Variance File KPLOT THP i Level 1 13 282 Level 2 17 942 Level 3 21 077 Level 4 Mm 23 692 Level 5 25 912 Level 6 28 34 Level lt 34 68
19. capabilities are included such as linear or logarithmic line plots contour and block i e pixel diagrams Device drivers for the HP Laser Jet series II HP plotters and dot matrix printers similar to Epson printers are included with GEOPACK Drivers for other printers and plotters can be written and included in GEOPACK The graphics programs supplied with GEOPACK produce intermediate quality output and are intended for quick and easy albeit rough graphic illustrations For the highest quality graphic output GEOPACK can be interfaced with any user defined graphics package so that custom diagrams can be developed Using the USER s Menu any commercially available graphics packages can be accessed while running GEOPACK A particular data file can be plotted using a commercial graphics package by either using an internal editor if one is included in the commercial graphics package or by writing a simple format translation program to create a new output file in the correct format 3 ECTION 2 wn SOFTWARE Zed CO PUT EN ER R EQUIRE G S programming languages an PC AT Compaq 286 386 version 3 30 or greater d runs Zenith etc using an and 640 K memory coprocessor but will use one if it is available increase operating efficiency directory GEOPACK also screen output to perform 4 Mbytes and appropriate monoch
20. default colors and names of default 1i e user defined programs Two files are used SYSETUP and SYSDEFLT for changing and storing the system default information SYSETUP is the basic file which MUST be present in the GEOPACK root directory This file contains the information which is written to the screen by this Utility program an example is 15 System Default Settings File RAM Disk or Temporary Directory C GEOPACK TMP Data Storage Directory C GEOPACK USER DATA Text Color Number 0 15 11 Border Color Number 0 15 6 Screen Mode 0 Black amp White 1 Color 1 Statistics Program MICROSTAT Word Processor or Text Editor EDT Line Type Graphics Program GRAPHER Contouring Graphics Program SURFE Data Base Management Program MFOXPLUS Esc quit Fl help F2 save I gt Home End Page Up Page Down Since paths are not given for any of the Default programs it is required that these programs reside in sub directories on the current MS DOS PATH so that they can be found from any sub directory by using the program name only It is also possible to specify the entire MS DOS path and program name PLEASE NOTE the programs MICROSTAT EDT GRAPHER SURFER and MFOXPLUS are commercially available programs and are not included with the GEOPACK system The Utility program writes out a file called SYSDEFLT which is used by the GEOPACK programs An example of this file is
21. except that the estimation grid is presented on the screen and each cell is filled with a color and or pattern in correspondence to the estimated value of the particular cell This provides another method for viewing the results of the data and gives a better feel of the coarseness of the grid system The pixel diagram which results from using this program can be printed by using the GRAPHICS COM utility supplied with MS DOS and the PRINTI SCREEN key 34 Zeal Description of the Disjunctive Kriging Menu Thu Jun 29 1989 07 47 45 am Return To Main Menu ATISTICAL PROGRAMS Main Menu Disjunctive Co Kriging Menu Return To Main Menu Set Program Parameters Hermit Coefficients DK Step 1 Estimates Co Kriging DK Step 2 Line Contour Diagram Block Contour Diagram Statistics Menu Variogram Menu Ordinary Co Kriging Menu F5 user menu Esc quit Fl help F3 util F4 view t Home End If the highlighted key D is typed or the light bar placed over the menu option Disjunctive Kriging Menu on the MAIN Menu and th nter key pressed th Disjunctive Kriging Menu is activated giving access to several programs for calculating estimates and conditional probabilities of the selected random func tion s in space Set Program Parameters Information on the setting of program parameters for disjunctive kriging can be found in Sections
22. for the last semivariogram or cross semivariogram graphed Contains the sample semivariogram values for variable 1 i e MOIST First saved file Contains the sample semivariogram values for variable 1 i e MOIST Second saved file Contains the sample cross semivariogram values for variable 1 with variable 2 i e MOIST vs TEMP First saved file Contains the model coefficients for the sample semivariogram values contained in VAR11 00 Contains the model coefficients for the sample semivariogram values contained in VAR11 01 Contains the model coefficients for the sample cross semivariogram contained in VAR12 00 Contains the semivariogram and cross variogram coefficients for use by the kriging and dis junctive kriging programs The default settings file for the kriging program This file is generated when the Default Settings program on the kriging menu is executed Contains the position the estimate and the estimation variance from the kriging program Temporary file containing the graphic data for the last kriging contour graph produced The default settings file for the disjunctive kriging program This file is generated when the Default Settings program on the disjunctive kriging menu is executed Contains the input data required by the dis junctive kriging program for variable i where
23. in A and the surface soil temperature in B using the Variogram Calculation Sample program and the data set C912 DAT Figure 3 3 2 The cross semivariogram function for the surface moisture content and the surface soil temperature using the Variogram Calculation Sample program and the data set C912 DAT Figure 3 3 2 Contour diagram of the estimated value of the electrical conductivity using the Ordinary Co Kriging and Block Contour Diagram programs Figure 3 3 3 Contour diagram of the estimation variance for electrical conductivity using the Ordinary Co Kriging and Block Contour Diagram programs vi wn ECTION 1 INTRODUCTION To use geostatistical techniques in the analysis of spatially correlated data generally requires the use of a computer to handle the large number of samples and carry out the lengthy calculations Unless someone is known who is willing to provide the necessary computer programs one is faced with the difficult task of finding purchasing or developing the required computer software Although there are a number of practicing geostatisticians who undoubtedly have access to the necessary programs these programs are not generally available or are proprietary codes Often the programs which are developed for research purposes are subject to limited availability and are difficult for others to use or modify for purposes other than those for which they were originally designed
24. select a second data set to work on the temporary directory must be cleared of a previous data set If you want to save the intermediate or final results from this previous data set use the PACK data set program described above 23 2 5 g Description of the Statisti Return To Main Menu Thu Jun 29 cs Menu 1989 07 47 45 am Main ATISTICAL PROGRAMS Menu Statistics Menu Return To Main Menu Sample Statistics Regression Analysis Kolomogorov Test of Distribution Least Squares Polynomial Percentiles of Data Variogram Menu Ordinary Co Kriging Menu Disjunctive Co Kriging Menu FS user menu If the highlighted key S is typed or the light bar placed over the menu option Statistics Menu on the MAIN Menu and th nter key pressed the Statistics Menu is activated On the Statistics Menu there are several programs from which you can choose These programs are intended to do the most basic statistical a packages which be a need for capabilities nalyses and are not i are available commerc to call i e run accessing a more comp ntended to replace comprehensive statistical ially Since it is anticipated that there will lete statistical package GEOPACK has built in a user defined statistical program from the USER s MENU access to the USER s M ENU is obtained by typing F5 Since the data format re
25. spending a little time becoming familiar with geostatistics end users will be able to include these geostatistical techniques in their work and research environments Ch tea 0 all Clinton W Hall Director Robert S Kerr Environmental Research Laboratory iii SUMMARY A comprehensive user friendly geostatistical software system called GEOPACK has been developed The purpose of this software is to make available the programs necessary to undertake a geostatistical analysis of spatially correlated data The programs were written so that they can be used by scientists engineers or regulators with littl xperienc in geostatistical technigues and still satisfy the requirements of more advanced users Using these programs and spending a little time becoming familiar with geostatistics the end user should be able to include these techniques in their work and research environments Acknowledgements The research and development of the computer software described in this report was supported in part by U S Environmental Protection Agency R S Kerr Environmental Research Laboratory Ada OK 74820 through an interagency agreement no DW 12932632 It has not been subject to the Agency s peer and administrative review and therefore may not necessarily reflect the views of the Agency and no official endorsement should be inferred Disclaimer of Warranty Although the authors of this s
26. 1 441 1963 Matheron G A Simple Substitute for Conditional Expectation The Disjunctive Kriging Proceedings NATO A S I Geostat 75 D Reidel Publishing Co Dordrecht Netherlands 1976 67 McBratney Regional Estimation of Soil Properties Soil Sci 135 177 183 1983 Morkoc F Myers Myers Myers PP Rep PiVay of Rendu J M Rendu 12 Rohlf F d co Russo D i T9 Russo D in 20 Russo D Russo D In Am Russo D A B and R Webster How Many Observations are Needed for J W Biggar D R Nielsen and D E Rolston Analysis of Surface Soil Water Content and Surface Soil Temperature using State Space Approach Submitted to Soil Sci Soc Am J 1985 D E Matrix Formulation of Co Kriging Math Gee 14 249 257 1982 D E A Simple Sufficient Condition for a Variogram Model to Yield Positive Variances Under Restrictions Comment Math Gee 16 431 432 1984a D E Co kriging New Developments G Verly et al Eds Geostatistics for Natural Resources Characterization Part 1 205 305 1984b P S C Rae J M Davidson and L C Hammond Use of Goodness fit Tests for Characterizing the Spatial Variability of Soil Properties Soil Sci Soc Am J 43 274 278 1979 An Introduction to Geostatistical Methods of Mineral Evaluation S African Inst of Mining and Metallurgy Northern Cape Printers LTD Kimberly South Africa 84pp 1978
27. 3 12515 3 034 27 00000 0 68900 44 11 314 3 838 27 00000 0 73400 45 15 537 3 034 27 00000 0 62900 46 T5 135 2 430 27 00000 0 68400 47 15 939 1 425 27 00000 0 33900 48 15 537 2 430 27 00000 0 77200 49 16 744 0 419 27 00000 0 53400 50 16 543 1 023 27 00000 0 23600 51 5 079 5 447 28 25000 0 60400 52 4 878 4 643 28 25000 0 46800 53 6 285 3 637 28 25000 0 65600 54 6 285 4 240 28 25000 0 71300 55 9 302 1 626 28 25000 0 58400 56 10 509 2 430 28 25000 0 79400 97 13 526 3 235 28 25000 0 66400 58 17 951 2 430 28 25000 0 72700 59 1 056 7 458 30 50000 0 19400 60 1 961 8 665 30 50000 0 67000 61 139 7 7 660 30 50000 0 66000 62 1 861 2 833 30 50000 0 53800 63 3 068 2 631 30 50000 0 33400 64 3 470 5 447 30 50000 0 63800 65 3 470 6 051 30 50000 0 55200 66 4 274 5 246 30 50000 0 15100 67 2 665 1 626 30 50000 0 50500 68 3 872 1 023 30 50000 0 43900 69 5 682 0 821 30 50000 0 53300 70 5 883 2 028 30 50000 0 62900 71 2 062 4 039 30 50000 0 41400 Several steps are required for conducting the geostatistical analysis and are described below The data set was created following the format instructions given in Section 2 4 a All user inputs are shown in Boldface type 45 Step 1 Select a Data Set To use GEOPACK a data set must be available Therefore the first step in using this program is to create a data set which is assumed to have been done and then start GEOPACK and select it 1 Select Data Set Utilities
28. 34 5S 16 et 76 6 17 14 129 4 18 14 934 4 19 4 374 11 20 5 983 12 21 1 961 10 22 5 280 6 23 9 906 4 458 453 263 665 464 056 855 045 654 866 671 654 660 654 240 442 682 2202 643 20 20 20 20 20 23 Zo 23 23 50000 50000 50000 50000 50000 50000 50000 50000 50000 50000 50000 26 26 26 24 24 24 24 24 24 24 24 24 24 24 00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 0 82800 0 94600 0 92400 1 16400 1 06700 0 79700 0 98900 0 89200 0 88900 0 69500 0 85500 0 73400 0 76900 0 80200 0 69600 0 67600 0 96300 0 81000 0 80500 0 81400 0 79600 0 69900 0 76000 44 EODIR US I ER DATA under the name 24 8 096 5 246 26 00000 0 64000 25 8 096 5 849 26 00000 0 94800 26 10 107 5 246 26 00000 0 48800 27 15 135 3 436 26 00000 0 59900 28 15 738 4 240 26 00000 0 57600 29 16 543 3 235 26 00000 0 94500 30 12 520 2 430 26 00000 0 75400 31 16 744 0 620 26 00000 0 67600 32 5 581 11 280 26 00000 0 79700 33 5 581 11 481 26 00000 0 54400 34 3 269 6 855 27 00000 0 39800 35 3 269 7 257 27 00000 0 37100 36 5 481 5 447 27 00000 0 81600 37 10 710 3 034 27 00000 0 31700 38 8 096 3 838 27 00000 0 67800 39 7 492 4 643 27 00000 0 65800 40 8 297 4 643 27 00000 0 76500 41 9 01 4 240 27 00000 0 78700 42 11 917 1 592 27 00000 0 73400 4
29. 59 8 843395 8 848577 8 856913 8 851551 o u K i ON ON amp wm Fa a i an died u ut n Figure 3 1 5 Contour diagram using the Ordinary Co Kriging and Block Contour Diagram programs In A and B respectively the estimated value for the decay rate and the estimation variances are illustrated 53 3 2 SALINITY IN A SOUTHWEST ARIZONA FIELD Description of Data This data set contains two random functions the electrical conductivity EC and the sodium adsorption ratio SAR The data was collected by Al Sanabani 1982 at 101 random locations on a lm by lm grid system in a 10 ha field soil type Typic Haplargid The 1 2 kg samples were placed in a beaker with distilled water and a saturated paste was made The solution was extracted from the paste and the EC of the solution measured A more detailed description of the data and techniques used to measure the EC and SAR is given in Al Sanabani 1982 This data set is included in the GEODIRS USER DATA directory under the name ECSAR DAT Step 1 Check Distribution of Data The hypothesis that the data were normally or lognormally distributed was tested using the Kolomogorov Smirnov KS test for goodness of fit Sokal and Rohlf 1981 Rao et al 1979 The KS test statistic was calculated and compared to the critical value at the 0 1 probability level This level was chosen to reduce the probability of the type II error namely the probabi
30. 7 Level 8 61 784 Figure 3 3 4 Contour diagram of the estimation variance for electrical conductivity using the Ordinary Co Kriging and Block Contour Diagram programs 65 REFERENCES AND SUGGESTED READING Abramowitz M and A Stegun Handbook of Mathematical Functions Dover Publications Inc New York 1965 Al Sanabani M Spatial Variability of Salinity and Sodium Adsorption Ratio in a Typic Haplargid Soil M S Thesis The Univ of Arizona Tucson 1982 Baafi E R Program User s Manual for Basic Geostatistics System Unpublished Report Dept of Mining and Gee Eng Univ of Arizona 50 pp 1982 Bell K R B J Blanchard T J Schmugge and M W Witczak Analysis of Surface Moisture Variations Within Large Field Sites Water Resour Res 16 796 810 1980 Bhattacharyya G K and R A Johnson Statistical Concepts and Methods John Wiley New York 639 pp 1977 Bower C A and L V Wilcox Soluble Salts In Methods of Soil Analysis Part 2 C A Black Ed Monograph No 9 Am Soc Agronomy Madison WI pp 933 951 1965 Burgess T M and R Webster Optimal Interpolation and Isarithmic Map ping of Soil Properties I The Semivariogram and Punctual Kriging J Soil Sci 31 315 331 1980a Burgess T M and R Webster Optimal Interpolation and Isarithmic Map ping of Soil Properties II Block Kriging J Soil Sci 31 333 341 1980b Burgess T M R Webst
31. C 3 xvariable j A plot of the data and regression line is provided as well as a comparison between the estimates and data values Percentiles of Data This program sorts the data set and gives several pre defined percentiles of the data 25 24 Delle Description of the Variogram Menu Thu Jun 29 1989 07 47 45 am Return To Main Menu ATISTICAL PROGRAMS Main Menu Variogram Menu Return To Main Menu Set Program Parameters Variogram Calculation Sample Automatic Model Fit Manual Model Fit Select Model s Edit Variogram Model File Statistics Menu Ordinary Co Kriging Menu Disjunctive Co Kriging Menu F5 user menu If the highlighted key V is typed or the light bar placed over the menu option Variogram Menu on the MAIN Menu and th nter key pressed the Variogram Menu is activated The programs on the Variogram Menu are intended to do the variogram analyses and should include the programming needed in the majority of cases Using the F5 key and interfacing to GEO EAS allows you to use the variogram program included in GEO EAS In some cases the GEO EAS program may include some feature not found in GEOPACK so it is advisable to check GEO EAS if you want a feature not currently supported in GEOPACK Since the data format requirements of GEOPACK are different from GEO EAS an interface is necessary and has been written into the GEOPACK system You must remember the names you give
32. EOEAS EXE color gt where the colors are given by the color numbers given below 0 Black 8 Grey 1 Blue 9 Light Blue 2 Green 10 Light Green 3 Cyan 11 Light Cyan 4 Red 12 Light Red 5 Magenta 13 Light Magenta 6 Brown 14 Light Yellow 7 White 15 Light White This program allows you to view the contents of a file To use this program type the following C VIEW lt border color gt t lt text color gt file name gt where the border and text colors are given in above Colors are either decimal as described above or hexadecimal using a format such as 0x1E This program allows you to manually edit the semi variogram coefficient file see the variogram menu and associated help screens for more information if it exists This program operates with the menu system and executes the necessary commands to create the hard coded and user definable menus This is an example of a user written interface to couple the GEO EAS geostatistical software to the GEOPACK system This program modifies that GEOPACK data file so the GEO EAS can read its contents MGEOCNVT EXE This is an example of a user written interface to couple the SHOWDIR EXE DEFLT EXE GEO EAS geostatistical software to the GEOPACK system This program modifies the GEO EAS output file so that GEOPACK can use the results for further analysis Thi
33. ER MEN place two in the newly create menu file each on a separate line 2 6 GEOPACK Enhancements 2 6 a Running GEO EAS Geostatistical Software The GEO EAS geostatistical software can be executed from within GEOPACK The GEO EAS programs are accessed by typing the F5 key and selecting the GEO EAS option Since the data set required by GEO EAS is formatted differently than GEOPACK there is an interface supplied to create a data set in GEO EAS format This data set will have the fil xtension EPA There is also an interface program to take the output from the GEOEAS kriging program and convert it to GEOPACK format This enables results to be printed and plotted using GEOPACK graphics capabilities ZA T S Description of GEOPACK Utility Programs GEOPACK contains a number of utility programs which can be used separately from the system to aid in alteration of the system or for use in a command line mode i e running the program without using the menu system A brief description of the function of each program and their use follows 40 Program Name HELP EXE GEOPACK EXE MSDOS EXE Description This program is used to call a particular help information section from a file For example if you want to print the help information concerning Theory of Variog
34. It is advisable copied to this subdirectory and could be accidentally deleted if only a drive is specified If ee Cr variety of programs unpredictable results Before GEOPACK will operate correctly several modifications to the computer must be since typically root directories ar used to store a any of these programs are deleted GEOPACK may produce the computer must have a specific This is done EC BAT file must EX configuration To install GEOPACK made These are described in more detail in the following sections 1 A temporary storage directory must be created automatically 2 An environment variable must be set The AUTO be altered 3 A system parameter file must be created This 4 is done automatically You will need to modify this file see Section 2 5 c to add the names of the editor line and contour graphics data base management system etc you have available 4 If you have a HERCULES graphics card you must run MSHERC COM prior to starting a GEOPACK session This program should be put in the AUTOEXEC BAT file 5 The ANSI SYS driver see your MS DOS manual must be installed in the CONFIG SYS file This is done by adding a statement like DEVICE C DOS ANSI SYS to the CONFIG SYS file Be sure that the correct path for ANSI SYS is used 242 Ds Temporary Storage Directory GEOPACK uses a temporary storage directory
35. Menu at Main Menu 2 Select Select a Data Set at Data Set Utilities Menu 3 To select the data set ither use the cursor keys to find the entry VIRUS DAT or type the name of the file on the keyboard If a number of files exist in this directory it is possible to move the cursor to the first or next file beginning with a specific letter by typing ALT letter i e hold the ALT key and type the desired letter Note the Select Data program automatically looks in the data directory This directory is specified in the SYSDEFLT file which can be altered using the Change System Default Settings program i e type F3 then C its the second line on the screen that follows Once the file VIRUS DAT has been selected GEOPACK reads in the data file and outputs to the screen the cutoff level and the number of available data points for the variables You are returned to the Main Menu Step 2 Check Distribution of Data The next step in the analysis is to determine if the data are normally distributed Although the kriging technique does not required the data to have a normal distribution and is a best linear unbiased estimator regardless of the distribution of the data the estimator is optimal whenever the data is normally distributed 4 Select Statistics Menu 5 Select Kolomogorov Test of Distribution 6 Select the appropriate data set in this case B decay The calculations are output to the screen At this time
36. Myers and D R Nielsen Geostatistical Methods Applied to Soil Science To be in Methods of Soil Analysis ASA 1985 Yates Marylynn V S R Yates A W Warrick and C P Gerba Modeling Virus Transport in the Subsurface using Geostatistics Applied and Environmental Microbiology 52 479 483 1986 69 Yates ay S R A W Warrick and D E Myers Disjunctive Kriging I Overview of Estimation and Conditional Probability Water Resources Research 22 615 622 1986 Yates S R A W Warrick and D E Myers Disjunctive Kriging II Examples Water Resources Research 22 623 630 1986 Yates S R Disjunctive Kriging III Cokriging Water Resources Research 22 1371 1376 1986 Yates S R A W Warrick and D E Myers A Disjunctive Kriging Program for Two Dimensions Computers and Geosciences 12 281 313 1986 Yates S R and A W Warrick Estimating Soil Water Content using Cokriging Soil Science Society of America Journal 51 23 30 1987 Yates Marylynn V and S R Yates A Comparison of Geostatistical Methods for Predicting Virus Inactivation Rates in Groundwater Water Research 21 1119 1125 1987 Yates S R A W Warrick A D Matthias and S Musil Spatial Variability of Remotely Sensed Surface Temperatures at Field Scale Soil Science Society of America Journal 52 40 45 1988 Yates S R and Marylynn V Yates Disjunctive Kriging as an Approach to Decision Making Soil
37. OPACK Data Set Utilities Menu Statistics Menu Variogram Menu Ordinary Co Kriging Menu Disjunctive Co Kriging Menu user menu From the main menu you can select one of several other menus using the cursor keys to move the light bar or highlighted region over the desired selection or by typing the highlighted character of the desired selection The function keys will display menus intended to offer help utilities and user defined applications Selecting an item from the MAIN menu will produce another menu containing programs or other options which are available for undertaking the statistical and geostatistical analyses A description of the available menus follows When leaving GEOPACK i e typing Q at the main menu another menu is produced which allows you to return to GEOPACK return to MS DOS leaving the intermediate data in the temporary storage subdirectory return to MS DOS saving the intermediate results to a packed file s Section 2 5 f or return to MS DOS and delete the intermediate results from the temporary subdirectory see Section 2 5 f 13 2 5 b Description of the HELP Menu F1 Thu Jun 29 1989 07 47 45 am Return to Main Menu EOSTATISTICAL PROGRAMS Main Menu EOPACK USER S MANUAL Quit GEOPACK Data Set Utilities Menu Return To Main Menu Statistics Menu Overview Of System Variogram Menu Installation Instructions Ordinary Co Kriging Menu F
38. PACK If you fail to do so the program will print an error message alerting you to thiserror the program does not explicitly state that the DEFAULT file is missing however The screen is similar to the screen shown in the section Select A Data Set described above 22 List Temporary Directory and View File This program allows you to list all the files that currently reside in the temporary directory To VIEW a file place the light bar on the desired file and type return Also by typing the F2 key additional information about the file is available The screen is similar to the screen shown in the section Select A Data Set described above Edit a Data Set This program allows you to edit a file Any file can b dited whether it exists or not Once this program is started you will see the directory listing of the SGEODIR directory i e the root of the geostatistical programs and you can select a file from this directory supply an alternate file and path or give a new directory name to see the listing of the new directory Remove All Files in Temporary Directory This command allows you to remove all the files in the temporary directory PLEASE NOTE THE TEMPORARY DIRECTORY SHOULD BE USED ONLY FOR THE GEOSTATISTICAL PROGRAMS SINCE THIS COMMAND WILL REMOVE ALL PROGRAMS IN THIS DIRECTORY or subdirectory Before you can
39. The data set must reside on the temporary directory prior to starting this program and be properly formatted for use with GEOPACK The newly created variables can be added to the file For example assume the data set has one variable called the moisture content If a new variable log moisture content is to be created it can be added to the file Pack Temporary Directory into File This program allows the archiving of the files residing in the temporary directory This is used if you want to store the intermediate results from GEOPACK for use at a later time Fach file is PACKED into a new file in the selected directory under a name you provide If a file with the same nam xists you will be asked if you want to overwrite it The screen is similar to the screen shown in the section Select A Data Set described above Unpack Temporary Directory from File This program allows you to retrieve the files that were previously packed using the program described above If you want to retrieve only a few of the files then use the program described below under EXTRACT A FILE The screen is Similar to the screen shown in the section Select A Data Set described above Extract a File From a Packed File This program allows you to retrieve one or more of the files that were previously packed using the PACK program described above Please note that you must retrieve the DEFAULT file if you plan to use GEO
40. am Will be Added whether a menu or a program is to be added The first step is to determin to GEOPACK If i programs or batch An example of crea GEODIR USER GEO directory o than specifying a program is that to G files ting a menu is the EAS where SGEODIR it is better to crea the geostatistical programs appears that the application to be added may require several a new menu containing these items G EO EAS M Th un the p aei EFOPACK data file in a format that can be read by G in the proper format fil interfacing program to create a new Next on this menu are the commands for starting the G is followed by a program which takes and rewrites the output in a format that G utines on s the use of GEOEAS it is better to put them into a n to utilize the GEOPACK ro commands concern specifically to run the GEOEAS progr the outpu EN file con is used by G e reason for creating a menu rather tained in the subdirectory CK to designate the root FOPA EFOEAS requires rewriting the EFOEAS This requires an rogram G the G am rathe on the USER menu since space is lin Step 2 Altering the USER MEN EFOEAS programs This t of the kriging program in GEOEAS EFOPACK can read This enables the user EFOEAS output Since each of these nenu
41. aneously Since only one model can be cross validated at a time the following method was used First the semivariogram for the surface moisture was cross validated This was followed by cross validating the surface temperature model Assuming that these semi variograms were not affected by the cross validation of the cross semivariogram they were fixed during the cross validation of the cross semivariogram Using this Cross Validation procedure the following variogram models yCh 0 00 34 0 1 exp h 8 23 for surface moisture y h 0 00 18 3 1 exp h 10 3 for cross semivariogram yCh 4 19 14 3 1 exp h 5 12 for surface temperatur 60 for h gt 0 were calculated The overall reduced mean and variance for this set of variograms is 0 0068 and 0 88 respectively Plots of the model variograms and the sample variograms are shown in the Figures Viewing the cross validated variogram models using the Save Model s Fit Models Manually option on the Variogram Menu indicates that either set of variogram models would be adequate representations of the spatial correlation structure Step 2 Create a Grid of Estimates Using CoKriging A total of 2500 estimates of the surface moisture content were obtained on a 2 by 2 meter grid system superimposed over the CAC field site using cokriging the auxiliary variable was the surface temperature Along with each estimate a value of the kriging variance was
42. are trying to determine the one you want to use for kriging To view the a semivariogram TYPE V RETURN and give the line number of the model you want plotted If you want to view several semivariogram then give the line numbers using the format 1 2 3 for lines 1 to 3 Note you can only view 3 or less models on one graph Manually Modeling a Semivariogram This option allows you to alter the coefficients of a saved semivariogram You must use the automatic fitting program prior to manually modeling a semivariogram since this gives you a good starting point for the coefficients If several model files are available you can see the sample semivariogram from which the model was derived by typing the F1 key If you choose to manually model the semivariogram you MUST place the model coefficients into the variogram model file manually as well unless you decide to use the automatically fitted values listed on the screen To manually model a semivariogram TYPE M RETURN change the coefficients shown at the bottom of the screen and type ESC to have the model and sample semivariograms plotted 30 Edit Variogram Model File This program allows the user to directly edit the file which stores the models for the semivariogram If a model is fitted to a sample semivariogram manually then the model coefficients must be manually entered into the variogram model file using this p
43. ble IV 2 as the second variable and so on The column in the data file that contains IVAR th random variable FORMAT 10 4x A6 The variable name for the I th variable NOTE the I th variable is the variable associated with IV I listed above See xamples given below for more information 10 Thi RECORD 73 FORMAT A30 Format specification for the data file This should be of appropriate form to read the data in the file F5 0 2F10 3 5X 1E10 2 ECORD 8 end see RECORD 7 DATA VALUE The data set should have a sample number or index X coordinates Y coordinates and the property s to be kriged Data is read until an end of file marker is found Therefore there should not be any blank lines in this part of the data file Note The sample no is assumed to be real Examples Of Data Sets s is a typical data file There are 4 random variables MOIST EMP SAND and OIL There are 119 positions where data was col lected only 4 positions are shown 4 119 1 2 3 9 4 6 7 MOIST I SAND OIL G5 0 12F10 3 1 2 118 119 6 0000 7 0000 46 8500 999 9990 56 5102 6 0000 10 0000 46 2900 5 9250 55 6444 24 0000 21 0000 46 3500 999 9990 54 4012 22 0000 24 0000 47 1400 999 9990 52 5845 11 Notes 1 In the abov xample the TEMP MOIST SAND and OIL are in columns 4 5 6 and 7 respectively However if you note line 5 and 6 you ll se
44. cedure of Marquardt 1963 This provides a first estimate for the coefficients to be used in a cross validation program and helps to auto mate the model fitting procedure If the least squares technique fails or other information is available which should be included in the model fitting process the traditional iterative method of manually selecting the model coefficients and viewing a graph comparing the sample values to the model can be used Linear Estimation GEOPACK includes programs to calculate the ordinary kriging and cokriging estimators in two dimensions along with their associated estimation variance Punctual and block kriging and geometric anisotropy are included There is a cross validation option which uses the kriging estimator in a jackknifing mode to cross validate the spatial correlation structure It is possible to include indicator kriging in an analysis by creating an indicator variable using a data transformation program supplied in GEOPACK Nonlinear Estimation Nonlinear estimators such as the disjunctive kriging and disjunctive cokriging estimators can be determined along with the estimation variance and the conditional probability that the value is greater than a specified cutoff level Up to 10 cutoff levels are allowed As with the linear estimation method this type of an analysis can be done on punctual or block support and may include anisotropy Graphics Outputs Various graphics
45. d SAR is given in Yates and Warrick 1988 This data set is included in the Available Data Sets option Type F5 followed by A and is named C912 DAT Step 1 Determining the Variogram As with all kriging methods some measure of the spatial correlation structure is necessary For cokriging a spatial correlation function is required for each random function as well a cross correlation function for each pair of random functions to be included in the analysis Since ordinary kriging is to be performed it is only necessary that the random functions be intrinsic i e it is no longer required that the variance be finite GEOPACK is used to determine the sample semivariogram by following the sequence given in Example 1 Next a model variogram is applied to the sample semivariogram For this example the automatic fitting procedure is used and yields the following exponential models y h 0 00 34 2 1 exp h 8 78 for surface moisture y h 0 00 18 4 1 exp h 10 8 for cross semivariogram y h 2 86 15 6 1 exp h 4 71 for surface temperatur for h gt 0 and are shown in Figures 3 3 1 and 3 3 2 The overall reduced mean and variance for this set of variograms is 0 0091 and 0 92 respectively This variogram model was used in the cross validation procedure listed on the Ordinary Co Kriging Menu which attempts to fit both the sample semi variogram and the reduced mean and variance simult
46. d th nter key pressed th Data Set Utilities Menu is activated On this menu there are several utilities which can be used to select edit or modify an existing data set to pack the contents of the temporary directory into an ARCHIVE file for later use or to extract all or part of the files from the archive Select a Data Set This program allows the selection of an existing data set The data set must be properly formatted for use with GEOPACK To create a new file s th editing program described below 20 Select a Data File C GEOPACK USER DATA zN C912 DAT ECSAR DAT EST DA VIRUS DAT A data set can be selected by either 1 typing in the file name or 2 by moving the light bar over the desired data set and typing the ENTER key Other subdirectories can be accessed in a similar manner to data files Please note that the symbol above indicates the subdirectory C GEOPACK USER and if a directory entry is preceeded by a W then the entry is a directory specification This program copies the requested data from its current path to the temporary directory creates a file called DEFAULT which contains the program name and its origination path GEOPACK uses the DEFAULT file to determine the proper name of the data file Both files i e the data file and DEFAULT must exist on the temporary directory before GEOPACK will work properly
47. e and creating the DEFAULT file which contains the data file name and origination path To use type SDATA from root of the geostatistical programs This program allows you to take the files on the temporary subdirectory e g RAM drive and store them in an archive file These files may be retrieved at a later time using one of the programs EXTRACT EXE SDATA EXE or UNPACK EXE To use type PACK from root of the geostatistical programs This program allows you to take an archived file and remove all the stored files back to the temporary storage drive i e RAM disk To use UNPACK from root of the geostatistical programs type This program allows you to take one or more stored files out of an archived file and place them on the temporary storage drive i e RAM drive You must extract the data file and the DEFAULT file before attempting to run GEOPACK To use EXTRACT from root of the geostatistical programs type up the xamples This program along with EVOKE allows you to call default text editor for editing the data base S for using EVOKE for use instructions This program allows you to list the contents of any direc tory on a floppy or hard drive The program also allows you to view a file To use type C LISTDIR lt dir name gt lt border color gt lt text 42 VIEW EXE VED EXE AUTO EXE MG
48. e that MOIST is specified as variable 1 followed by TEMP SAND and OIL This changes the order for the IV i and NAM i data 2 Since all the random variables were not sampled at every location some method for delineating missing data is needed In the abov xample missing data is specified by entering a large number i e 999 9990 When executing a program in GEOPACK it will ask you the CUTOFF value for delineating missing data and you should give a value slightly smaller than 999 9990 but larger than any valid data value for example 999 or 900 This example data file is the same as the one abov xcept there ar no sample numbers To alleviate this problem the first column of the data file is specified as the sample number i e they are all 0 4 119 1 2 3 5 4 6 7 MOIST TEMP SAND oil G1 0 F9 3 12F10 3 6 0000 7 0000 46 8500 999 9990 56 5102 6 0000 10 0000 46 2900 5 9250 55 6444 22 0000 24 0000 47 1400 999 9990 52 5845 12 2 5 THE MENU SYSTEM During installation you are asked for the name you want to use to start the geostatistical programs where the default name is GEOPACK After starting the program using the selected name the first menu displayed is the MAIN menu 2 5 a Description of the MAIN Menu Thu Jun 29 1989 07 47 45 am Return to MS DOS with prompt to save settings and files EOSTATISTICAL PROGRAMS Main Menu Quit GE
49. e the MODEL semivariogram file 29 Save Model s Fit Model Manually This program displays the model semivariogram coefficients that have been modeled using the automatic fitting program and allows the user to select the best model to be saved in a file for use by the kriging program The program allows you to save view and manually model the semivariogram Each operation is described below Saving a Semivariogram The semivariogram model can be saved to the file which then becomes available to the Ordinary Co kriging and Disjunctive Co kriging programs This must be done prior to kriging otherwise the kriging program will not have a variogram model to use in the calculations If the semivariogram models were fitted to the sample semivariogram using the least square method i e automatic fitting procedure then the semivariogram model should be cross validated prior to kriging To do this use the Cross Validation option on the Ordinary Co Kriging menu To save the a semivariogram type S RETURN and give the line number of the model you want saved If no semivariogram model coefficients are saved the kriging program will not work properly and an error message will be printed out stating that no semivariogram model coefficients were found Viewing a Semivariogram This option allows you to view a saved semivariogram You might want to do this if you have saved many semivariograms and
50. en ite d States Robert S Kerr Environmental ie ae SEPA G eosta ti stics for Waste Management A User s Manual for the GEOPACK Version 1 0 Geostatistical Software system yyy gt EPA 600 8 90 004 January 1990 GEOSTATISTICS FOR WASTE MANAGEMENT A User s Manual For the GEOPACK Version 1 0 Geostatistical Software System by S R Yates USDA ARS U S Salinity Laboratory Riverside CA 92501 and M V Yates Department of Soil and Environmental Sciences University of California Riverside CA 92521 Interagency Agreement No DW12932632 Project Officer David M Walters Processes and Systems Research Division Robert S Kerr Environmental Research Laboratory Ada Oklahoma 74820 ROBERT S KERR ENVIRONMENTAL RESEARCH LABORATORY OFFICE OF RESEARCH AND DEVELOPMENT U S ENVIRONMENTAL PROTECTION AGENCY ADA OKLAHOMA 74820 DISCLAIM ira re The information in this document has been funded wholly or in part by the United States Environmental Protection Agency under interagency agreement No DW 12932632 to the United States Department of Agriculture United States Salinity Laboratory It has been subjected to the Agency s peer and administrative review and it has been approved for publication as an EPA document Mention of trade names or commercial products does not constitute endorsement or recommendation for use ii FOREWORD EPA is charged by Congress to protect the Nation s land
51. enu are given in Section 2 5 k 2 3 b The Function Keys and Cursor Movement The function keys Fl F3 F4 and F5 can be used at any menu in the following manner F1 Help At menu and program levels In programs other F keys also display help information and are indicated when they are active F3 Utility Menu F4 View previous screen F5 User Menu User defined programs menus etc Makes GEOPACK adaptable A complete description of th ntries on each of the menus that are accessed by the Function keys is given in Section 2 5 The Menu System The cursor i e the light bar or highlighted selection can be moved by using the following cursor control keys Home End PgUp PgDn Arrow Keys If these keys are located on the keypad the NUM LOCK key must be turned off A menu entry can also be selected by pressing the letter or number that is highlighted in the desired entry 2 3 c File Naming Convention Whenever a data set is selected this data set can be located in any subdirectory on any disk a file is created in the temporary storage directory and is called DEFAULT This file contains two lines the first gives the selected file name and the second the origination path of the file A copy of the selected file is written to the temporary storage drive as well These two files DEFAULT and the data set are required before GEOPACK will run properly All the program
52. er and A B McBratney Optimal Interpolation and Isarithmic Mapping of Soil Properties IV Sampling Strategy J Soil Sci 31 643 659 1981 Burrough P A Multiscale Sources of Spatial Variability In Soil I The Application of Fractal Concepts to Nested Levels of Soil Variation J of Soil Sci 34 577 597 1983a Burrough P A Multiscale Sources of Spatial Variability In Soil II A Non Brownian Fractal Model and its Applications in Soil Survey J of Soil Sci 34 599 620 1983b Carr J R D E Myers and C E Glass Co kriging A Computer Program Comp and Gee 1984 Clark I Practical Geostatistics Applied Sci Publ LTD Essex England 129 pp 1979 David M Geostatistical Ore Reserve Estimation Elsevier New York 1977 66 Davis B M Indicator Kriging as Applied to an Alluvial Gold Deposit Geostatistics for Natural Resources Characterization Part I G Verly et al Eds pp 337 348 1984 Dunn M R A Simple Sufficient Condition for a Variogram Model to Yield Positive Variances Under Restrictions Math Gee 15 553 564 1983 Dunn M R A Simple Sufficient Condition for a Variogram Model to Yield Positive Variances Under Restrictions Reply Math Gee 16 443 434 1984 Gajem Y M A W Warrick and D E Myers Spatial Dependence of Physical Properties of a Typic Torrifluvent Soil Soil Sci Soc Am J 45 709 715 1983 Hatfield J L J P Millard and R G G
53. estimates of the selected random function s in space You can use the F5 key to interface to GEO EAS or other programs which allows you to use the ordinary kriging program for one random function included in GEO EAS Set Program Parameters Information on using the setting of the program parameters for kriging is similar to that given in Section 2 5 i An example of the screen generated by the Set Program Parameters program is given below More information about the parameters can be found by starting this program and using the F1 key 32 Kriging Parameter Settings File Est Loc in File Y N Anisotropy Ratio Maximum Search Radius f Anisotropy Angle Contour File Y N Number Contour Levels Enable Graphic Option Save Intermed Results ESTIMATE GRID P B ORIGIN No of Points X Width Betw Pts X No of Points Y Width Betw Pts No OF VARIABLES FAREST NEIGHBORS Estimate Var 1 Estimate Var 1 Auxiliary Var 1 iliary Var 1 Auxiliary Var 2 iliary Var 2 Auxiliary Var 3 iliary Var 3 Auxiliary Var 4 iliary Var 4 BLOCK KRIGING DISCRETIZATION BLK COVAR O default T of Cells X Width of Cell X of Cells Y Width of Cell Y eg e Cross Validation GEOPACK provides you with a program that allows you to cross validate the model for the spatial correlation structure The cross validation tech
54. field for that parameter During execution you will be asked to provide only that value In this manner you will only have to answer the necessary questions during execution Spatial Correlation Function Parameter Settings File Data File Name Enable Graphics Options i e G Y N Save All Sample Variogram Functions Y N Data Cutoff Value Number of Lagged Distances Distance Between Lagged Distances Width of Lagged Interval Width of Angle Class Number of Directions Angle for Direction Number 1 Angle for Direction Number 2 Angle for Direction Number 3 Angle for Direction Number 4 27 Variogram Calculation Sample This program calculates the sample semivariogram or cross semivariogram for a spatially dependent two dimensional random function There are two ways that the results from the sample semivariogram program can be saved The easiest method is to specify in the Parameter Settings file to save all sample semivariograms i e Place a Y in the appropriate field When this is done every time the sample semivariogram program is run the results will be stored on the temporary subdirectory Since 15 files may be saved at any time you will most likely never run the program more than 15 times so saving every file will not produce a problem If you should create 15 files and wish to save additional sample semivariograms you can delete files that you do not expect to use
55. gives 4 0 dS m as a critical value of EC for many plants therefore this value or the 1n 4 0 dS m was used for the critical value i e Z in subsequent analyses For all cases a maximum of 5 nearest neighbors within a radius equal to the range of the variogram were used in the estimation process Next the results were contoured to show the spatial distribution of the electrical conductivity and illustrated in Figure 3 2 2 Step 6 Create a Grid of Conditional Probability Estimates The disjunctive kriging estimator can also be used to determine th conditional probability that the unknown value is greater than a specified cutoff value An example of this is given in Fig 3 2 3 where the conditional probability that the In EC is greater than 1n 4 0 respectively is contoured 56 From this figure one can see that the zones of high probability coincide with areas of high Il1n EC Although the shapes of the high probability zones are similar to the shapes of the In EC contours in Fig 3 2 2 two points with the same estimated value of In EC do not always produce the same conditional probability For more information see Yates et al 1986 Salinity Le 8 9 8 8 8 77 8 67 8 7 BA 8 3 8 2 BL Senivariogran 8 43 4 ui 132 248 Distance n Figure 3 2 1 The semivariogram function for the natural logarithm of the electrical conductivity using the Variogram Calculation Sample program and
56. he data Using e CUTOFF missing data can be excluded from any analysis To accomplish this set any missing data in the data file to a large number e g 99999 99 This number must be larger than the numeric value of any variable To exclude these large num bers set the CUTOFF value to a number slightly SMALLER than the missing data number e g 99999 00 Then the mis sing data will not be used by any program RECORD oh IINX IX TY IV 1 IV IVAR RECORD Gs NAM I FORMAT 1315 The column in the data file that contains the sample number If no sample is avail able the program can be made to read a blank field as zeros In general this will not cause any problem in running the programs The column in the data file that contains the X coordinate data See examples given below for more information The column in the data file that contains the Y coordinate data See examples given below for more information The column in the data file that contains one of the random variables The sel ection of the first second etc random variable is arbitrary The easiest way to specify these is to sequentially num ber the random variables in the order from left to right that they appear in the data file The program uses the order you specify here as the order the vari ables will be listed out on the screen If you want to change the order then give IV 1 as the 1st varia
57. he semivariogram function Figure 3 1 2 Example output from the Automatic Model Fit program The solid line is an spherical model that was fitted to the sample semivariogram Figure 3 1 3 Example output from Manual Model Fit Select Model s program in A and the Edit Variogram Model File in B Figure 3 1 4 Contour diagram of the estimated value of the decay rate using the Ordinary Co Kriging and Line Contour Diagram programs is illustrated Figure 3 1 5 Contour diagram using the Ordinary Co Kriging and Block Contour Diagram programs In A and B respectively the estimated value for the decay rate and the estimation variances are illustrated Figure 3 2 1 The semivariogram function for the natural logarithm of the electrical conductivity using the Variogram Calculation Sample program and the data set ECSAR DAT Figure 3 2 2 Contour diagram of the estimated value of the electrical conductivity using the Disjunctive Co Kriging and Block Contour Diagram programs Figure 3 2 3 Contour diagram of the conditional probability that the estimated value of the electrical conductivity is greater than the natural logarithm of 4 dS m i e 1 38 log dS m using the Disjunctive Co Kriging and Block Contour Diagram programs This figure shows the actual screen position of the contour levels window when displayed Figure 3 3 1 The semivariogram function for the surface moisture content
58. i is the variable number This file is created by executing the Hermite Coefficients program on the disjunctive kriging menu Contains the position the estimate estimation variance and conditional probabilities if any from the disjunctive kriging program Temporary file containing a contour representation of one of the output data 8 types contained in DPLOT TMP i e it has the last disjunctive kriging graph produced 2 4 DATA FILI GI 2 4 a Format Instructions To operate GEOPACK a data file must be created in the proper format Using a text editor or word processor a data file can be entered or modified for use with GEOPACK For GEOPACK to function properly the data set must contain at the minimum 1 one or more spatially dependent random variable s i e soil temperature moisture hydraulic conductivity concentration etc and 2 an x and y position for each value of the random variable s A data file must be created in ASC format using the following standard FORTRAN formatting instructions ECORDS 1 3 FORMAT A76 A76 A76 Three lines of title RECORD FORMAT 215 F10 3 The total number of random variables in the data set These are values of the parameters that will be used in obtaining estimates etc e total number of positions i e and Y coordinate pairs in the file CUTOFF e value given to this variable is the ximum allowed value for t
59. ile Formatting Instructions Disjunctive Co Kriging Menu Basic System Operation Menu Help Utilities in GEOPACK Adding User Programs and Menus F5 user menu Esc quit Fl help F3 util F4 view t Home If the Fl key is pressed from any menu the HELP Menu is activated On the HELP Menu there are several help files you can access In general the information in the User s Manual and some theory of geostatistics can be found on the HELP menu 14 2 5 c Description of the UTILITY Menu F3 Thu Jun 29 1989 07 47 45 am Return to Main Menu ISTICAL PROGRAMS Main Menu Quit GEOPACK Statistics Menu Variogram Menu Return To Main Menu Ordinary Co Kriging Menu Change System Default Settings Disjunctive Co Kriging Menu DOS Shell Execute an MS DOS Command Graph Most Recent Graphic Program Structure F5 user menu If the F3 key is pressed from any menu the UTILITY Menu is activated On the UTILITY Menu there are several programs available to alter basic GEOPACK parameters run MS DOS commands while inside GEOPACK and view the current GEOPACK program structure Each utility is described in more detail below Change System Default Settings This Utility allows you to change the default settings which are used by GEOPACK The default settings include the path specifications device names screen type
60. iogram Menu 21 Select Manual Model Fit Select Model s 22 You now select the desired file by hitting Enter 23 A summary of the models that you have run on that data file is then shown Type S to save the correlation model that you want to krig 24 You are returned to the Variogram Menu Step 4 Create a Grid of Estimates Using Ordinary Kriging The final step in this example is to obtain a grid of estimates using the data set and the model of the spatial correlation structure An estimate can be made at any point in the field of interest In general estimates made far from any data points will have a higher estimation variance i e there is less confidence that the estimate is close to the true value compared to estimates made close to data points If an estimate is made at the same coordinates as one of the data points in the data set the estimated value will exactly equal the data value at that point and the estimation variance will be zero This behavior indicates that kriging is an exact interpolator 25 Select Ordinary Kriging You will be asked several questions unless you have modified the Default Settings file to avoid this 47 26 Several screens showing the output from the kriging calculations will be output to the screen Once again at the Kriging Estimates for Decay screen you are given the opportunity to Jump ahead and bypass seeing the output of this program 27 When the program is fi
61. le called USER MEN which is located in the root directory of the geostatistical programs i e if the default directory was chosen it would be C GEOPACK The necessary information for modifying the GEOPACK program is given under the heading Adding User Defined Programs and Menus on the User s Manual Help screen i e type Fl 18 A brief description of the menu options which are provided with the original GEOPACK system follows Statistics Package Default This feature allows you to run a default statistics package during a GEOPACK session The default statistics package is defined i e the path and name specified by using the system default setting program To start this program type F3 and select Change System Default Settings In the present example it e l is assumed that the GEOPACK data set will have to be modified to a format that th default statistics package can read Therefore selecting this option wil produce another menu which will let you create a file in the proper format Note this program may have to be changed for other statistics programs and run the statistic program The default statistics menu is located in the subdirectory SGEODIR USER DSTAT under the file name DSTAT MEN Graphics Menu This feature allows you to run one of several graphics programs during a GEOPACK session When this option is selected an
62. le or position number the sample number must be a real number During execution of GEOPACK whenever additional storage space i e memory is required by a program the space is obtained from the large storage array If attempts are made to use more memory than is available an error message is printed out giving the memory status From this information a decision can be made on how to reduce the memory requirements to allowable limits i e reducing the number of variables or samples considered etc The GEOPACK system includes programs to do the more common statistical and geostatistical analyses The system is estimation oriented in that if the ordering in the menu system is followed a grid of estimates for the selected variable in the data set will result A description of the various components of the system follows Help Facilities The program includes on line help facilities to provide the user with information concerning the operation of the program data requirements conventions definitions run time errors missing files etc that are encountered during execution At the menu level the help information is of a general nature During execution of a program the help is more specific such as defining a term User Defined Programs GEOPACK includes a feature which makes it simple to access any user defined program i e program not included with GEOPACK for generating statistics line graphics s
63. lity of incorrectly selecting the null hypothesis Rao et al 1979 For a sample size greater than 30 the critical value at the amp 0 1 probability level can be obtained from the asymptotic expansion Rohlf and Sokal 1981 Rao et al 1979 K S 0 805 Jn The results of the KS test indicate that the original and log transformed data are from lognormal and normal distributions respectively at the 0 1 probability level Therefore a lognormal transformation will cause a data set to have a normal distribution The KS test statistic calculated from the data sets were 0 197 and 0 065 for the original EC and transformed 1nEC data respectively The associated critical value is 0 080 and was calculated by Eq 1 for n 101 Since the data are lognormally distributed they will be transformed to a data set with a normal distribution by taking the logarithm of each datum This new data set will be used for the geostatistical analyses Step 2 Transform the Data Set The data set can be transformed by using the Modify an Existing Data Set option on the Data Set Utilities Menu The steps necessary to use this program to add a random function called In EC by taking the logarithm of the EC data are The allowable transformations can be viewed by typing F1 Help before selecting the variable to modify Place the lightbar over the data set i e EC to be transformed Type Enter 2 Move the lightbar over
64. ly created menu must be created using the methods described above It is probably best to start with an existing menu command file e g USER MEN GEOEAS MEN or equivalent to act as a template changing only those lines that are needed guide for setting up the command file This will provide a In the USER MEN file the call to the new menu is made as follows assuming that a new subdirectory called NEWDIR has been created with the following path SGEODIR S USER NEWDIR and that the command file for the new menu is called NEWMEN MEN place a descriptive message for the menu here NEWMEN Menu A oe GEODIR user men COMSPEC S c cd GEODIR user newdir ae A ole GEODIR user newdir NEWMEN MEN The commands necessary to run one or more programs from the new menu ar as follows it is assumed that the new program is called N Quit Menu Quit Run _NEWPRG place a descriptive message for what the program doe GEODIR user newdir NEWPRG The above instructions should be adequate for modifying G new menu and program s 39 EWPRG s here FOPACK to include the 2 08 le Trouble Shooting If an error should occur while attempting to add a program or menu to GEOPACK try one of the remedies listed below 1 The newly created USER menu entry does
65. nique used is a semi quantitative technique based on kriging and is used to evaluate whether the covariance function or variogram is appropriate for the experimental data The method involves estimating the value of the random function of interest at every known sampling location but excluding the known value from the estimation process the known value is excluded because kriging is an exact interpolator Using all the pairs of actual and estimated values various quantities can be calculated and used as an indication of the quality of the model spatial correlation function Ordinary Kriging and Cokriging The program GEOKRIG is used for kriging and cokriging GEOPACK allows up to 10 variables to be used for cokriging although it is advisable to use 4 or less random functions in practice If more than 5 random functions are used the default settings program cannot be used while running the kriging program since it only allows you to input 1 primary and 4 auxiliary random functions A large static array of 10000 words is partitioned for storage of input data the kriging matrix etc so there is a limit to the size of problem that can be executed with this program 33 GEOPACK allows you to create estimated values in one of two manners either on a grid system or by reading a file of x and y coordinates This latter method is useful if irregularly spaced estimates are required Estimates on a Grid The first method i
66. nished you are returned to the Ordinary Kriging Menu where you select Line Contour Plot 28 You are given the choice of plotting the estimated value or the variance In this case we choose A and the following contour plot is shown on the screen 29 You are given the option to add labels to the plot as before 30 After Exiting this program you are returned to the Ordinary Kriging Menu 31 This time we select Block Contour Plot 32 Again we choose A to plot the estimated values and the output looks like the following 48 a o oa DATE 09 01 1989 TIME 09 06 am A No OF SEMIVARIOGRAM LAG COUPLES DISTANCE DECAY DECAY 1 11 41 0243 1444 2 125 1 23 0292 0649 3 232 2 38 0366 y EZS 4 230 3 54 0415 OD RE 25 o 5 249 4 65 0426 1603 6 241 5 83 0437 633 7 216 6 95 0424 1621 8 193 Sil 0379 a 7 9 160 9 38 0342 1586 10 175 10 50 0406 1680 1a 137 11 66 0574 2497 12 146 12 77 0426 21559 Strike a key when ready X R O H Virus Data 8 85 4 045 gt lead _ gran 8 03 Senivario 4 83 8 823 8 82 Distance km Figure 3 1 1 Example output from Variogram Calculation Sample program for the data set VIRUS DAT In A and B respectively are the tabular values and a plot of the semivariogram function 49 Virus Data AN 8 84 8 84 ASN 8 83 8 82 8 82 AJN 8 8 8 88 gran ivario Sen Distance km
67. not show up on the USER menu This might occur if the wrong menu data file was altered The proper file to alter is GEODIRSUSER MEN Also only 11 entries can be placed on one menu If you wish to have more than 11 entries you will have to create an additional menu or move some of the programs to other menus if they exist 2 The newly created menu does not run when selected from the USER menu This is probably due to an improper path file name combination Make sure that the path and file names are correct If an error message is printed out by the program it is often lost because the menu reappears on the screen too quickly The error message or other information can be seen by typing the F4 key 3 The newly created menu does not have any entries on it and an error message Abort Menu Menu Data Not Found is printed to the screen This is caused because the menu program cannot find the newly created menu data file This may be due to changing directories before the new menu is placed on the screen You should check to make sure that the commands in the User Menu and the new menu ar appropriate for what you are trying to do 4 To get back to the USER MENU located at the right hand side of the screen you have to type two quits This is caused because you have popped an additional USER MEN on to the screen and the newly created menu only deletes one of the USER MEN when you quit the menu To delete two US
68. ntour Diagrams Line and block contour diagrams are also available from the Disjunctive Kriging Menu For more information concerning these programs see the description under the Kriging Menu above 2 5 k Modifying and Adding Menus It is possible to tailor GEOPACK to an individual s needs by adding programs or menus to the USER menu accessed through the F5 key If the program to be added to the system requires the use of the data set or any of the output files produced by GEOPACK read the help information under the heading SYSTEM OPERATION on the main HELP menu The information concerning the files their contents formats naming conventions etc is given by this help sequence The following steps are used to add a program or menu to GEOPACK Several examples are included in GEOPACK and can be found by typing the MEN files It is usually easier to start with copy of an existing MEN file or portion thereof as a template and make the required modification s to the template To add a single executable program is very easy since only a few lines must be added to an existing MEN file To add an additional menu requires creation of a complete MEN file and therefore is somewhat more difficult If a new menu is to be created it is generally a good idea to place the MEN and executable files is a new subdirectory 36 STEP 1 Determining Whether a Menu or a Progr
69. oettelman Variability of Surface Temperature in Agricultural Fields of Central California Photo Eng and Remote Sensing 48 1319 1325 1982 Hatfield J L M Vauclin S R Vieira and R Bernard Surface Tempera ture Variability Patterns with in Irrigated Fields Agric Water Manage 8 429 437 1984 Journel A G and Ch J Huijbregts Mining Geostatistics Academic Press New York 1978 Journel A G The Place of Non parametric Geostatistics Geostatistics for Natural Resources Characterization Part I G Verly et al Eds pp 307 335 1984 Journel A G Fundamentals of Geostatistics in Five Lessons Department of Applied Earth Sciences Report Stanford University Stanford CA 1988 Kim Y C D E Myers and H P Knudsen Advanced Geostatistics in Ore Reserve Estimation and Mine Planning Practitioner s Guide Report to the U S Energy Research and Development Administra tion Subcontract No 76 003 E Phase II 1977 Lemmer I C Estimating Local Recoverable Reserves Via Indicator Kriging Geostatistics for Natural Resources Characterization Part I G Verly et al Eds pp 349 364 1984 Marechal A The Practice of Transfer Functions Numerical Methods and Their Application Proceedings NATO A S I Geostat 75 D Reidel Publishing Co Dordrecht Netherlands 1976 Marquardt D W An Algorithm for Least squares Estimation of Non linear Parameters J Soc Ind Appl Math 11 43
70. oftware hav ndeavored to produce accurate reliable and correct software this software including instructions for its use is provided as is without warranty expressed or implied Furthermore the authors do not warrant guarantee or make any representations regarding the use or the results of the use of the software or written materials concerning the software in terms of correctness accuracy reliability currentness or otherwise The entire risk as to the results and performance of the software is the sole responsibility of the user If the software or written materials are defective the user and not the author agents or employees assume the entire cost of all necessary servicing repair or correction Compaq is a registered trademark of the Compaq Corporation IBM is a registered trademark of the International Business Machines Inc Microsoft and MS DOS are registered trademarks of the Microsoft Corporation Hercules is a registered trademark of the Hercules Corporation JZenith is a registered trademark of the Zenith Corporation HP ThinkJet and LaserJet are registered trademarks of the Hewlett Packard Company iv TABLE OF CONTENTS Foreword Summary Acknowledgements List of Figures Section 1 Introduction 3 Kos 2 Software Degcitiption Sid dperabion iastract tows 1 Computer Requirements 2 Installing GEOPACK a Ins
71. on of other geostatistical programs such as GEO EAS reference so the features of this and other programs can be accessed Examples showing how these geostatistical programs can be used in the analysis of spatially correlated data can be found in Yates et al 1986 a b c Yates 1986 Yates and Warrick 1987 Yates et al 1988 and Yates and Yates 1988 1989 For individuals interested in learning geostatistical techniques a number of texts are available and include Clark 1979 Journel and Huijbregts 1978 Journel 1988 and David 1977 GEOPACK geostatistical software system is a package of programs for conducting analyses of the spatial variability of one or more random functions The system is menu driven and simplified so that a minimum number of input data are needed The programs also limit the amount of intermediate results printed to the screen or the printer GEOPACK uses dynamic allocation of memory so that data sets with a wide range of variables and positions can be used without having to alter the program A large storage array currently set to approximately 10000 storage locations is partitioned based on the number of samples and variables so that there is little wasted space compared to defining the arrays to have a fixed number of samples and variable One limitation is that GEOPACK allows data base i e a data file to contain a maximum of 10 variables plus their x and y positions and a samp
72. one of the Unused markings and type Enter A window will pop up in which the name for the new data set can be entered In this case the new data set will be called Iln EC 54 3 Type in the transform equation which for this example is y log x natural logarithm and type a F4 to start the transformation process Once completed both the EC and In EC data sets will exist in the data file 4 To save the transformation results type F2 and either O to overwrite the data file or B to save a backup copy of the old data file If you decide you do not want to save the new data set the type ESCAPE and you will be asked if you want to leave the program without making any changes 5 To exit type ESCAPE Step 3 Determining the Variogram As with all kriging methods some measure of the spatial correlation structure is necessary For disjunctive kriging the appropriate function is the auto correlation which requires a second order stationary hypothesis i e the variance must be finite An easy method for determining the autocorrelation from the semi variogram is to use the following relationship p h 1 y h y e which is done automatically when using the disjunctive kriging program Using GEOPACK to determine the sample semivariogram by following the sequence given in Example 1 Next a model variogram is applied to the sample semivariogram For this example the automatic fit
73. other menu is produced which has three options The first is to execute the GEOPACK graphics program and the other two are the default line and contour graphics programs Data Base Management System Default This feature allows you to run a default data base management system during a GEOPACK session GEO EAS This feature allows you to run GEO EAS during a GEOPACK session Available Data Sets This option allows you to select a data set from a subdirectory used solely for storing data sets The subdirectory specification is GEODIR USER DATA and the program SDATA EXE is used for displaying and selecting the data sets located in the directory for additional information see Select a Data Set in Section ZOE sz 19 Dros Les Description of the Data Set Utilities Menu Thu Jun 29 1989 07 47 45 am Return To Main Menu EOSTATISTICAL PROGRAMS Main Menu Data Set Utilities Menu Q Return To Main Menu Select a Data Set odify an Existing Data Set Pack Temporary Directory into File Unpack Temporary Directory from File Extract a File From a Packed File List Temporary Directory and View File Edit a Data Set Delete All Files in Temporary Directory Esc quit Fl help F3 util F4 view F5 user menu t Home End If the highlighted key U is typed or the light bar placed over the menu option Data Set Utilities Menu on the MAIN Menu an
74. quirements of GEOPACK may package an interface mayb format When this is necessary be different from the commercial statistics necessary to rewrite the data file in the appropriate PG is advisable to have the Default Statistic Package option on the USER menu cal start commands on it Sample Statistics This program calculates the d statistics includ the number of standard deviation skew kurtosis An example is provided in the file l up another menu which has the interface and SGEODIR S USER MEN escriptive statistics for the data set These samples used the mean median variance maximum and minimum values of the data set 24 Regression Analysis This program calculates the linear regression coefficients A and B for the linear model variable i A Bxvariable j jz i A plot of the data and regression line is provided as well as the coefficient of determination and a comparison between the estimates and data values Kolomogorov Test of Distribution This program calculates the Kolomogorov Smirnov test statistic for a normal distribution Other distributions can be tested for by transforming the variable of interest using the Modify a Data Set command on the DATA SET UTILITIES MENU Least Squares Polynomial This program calculates the nonlinear regression coefficients C i for the polynomial model variable i C 1 C 2 xvariable j
75. rams the HELP program could be used as follows C HELP VARI HLP THEORY HLP where VARI HLP is the help information desired and THEORY HLP is the file containing VARI HLP This program displays the first screen giving the GEOPACK name This program also determines where the call to GEOPACK is made i e the subdirectory where GEOPACK is typed so that after leaving the program you will be returned to that directory This program allows you to execute a DOS command while run ning GEOPACK DOSSHELL EXE This program allows you to leave GEOPACK in a DOS shell and MENU2 EXE EVOKE EXE temporarily suspend execution of GEOPACK When finished ex ecuting DOS commands you reenter GEOPACK by typing EXIT This is the menu program This program is used to execute a program when it is desired that system parameters be passed to the program Note system parameters are set by the user and are difficult to hard program This program is particularly useful when altering i e adding additional programs GEOPACK since it enables you to pass system parameters to other programs without having to know their value For example to run a C program and passing the location of the temporary directory the border color and the text color use EVOKE lt prog name gt TEMPDIR BORD S TEXT EVOKE EXE substitutes the true values for TEMPDIR S BORD and S
76. rogram Variogram Editor File G TEST VAR Variables Model Nugget Sill Nugget MOIST MOIST Exponential alba sal MOIST TEMP Exponential 2 999 MOIST SAND None TEMP MOIST Exponential 2 999 TEMP TE Exponential 15 003 SAND TI SAND SAN None None Pos TEMP SAND None P D Esc Exit Fl Help F2 Save et gt Home End Page Up Page Down If no semivariogram model coefficients are saved the kriging program will not work properly and an error message will be printed out stating that no semivariogram model coefficients were found To correct this error use the Save Model s Fit Model Manually program to save the semivariogram model coefficients for the random functions of interest 31 Oi oein Description of the Kriging Menu Thu Jun 29 1989 07 47 45 am Return To Main Menu GEOSTATISTICAL PROGRAMS Main Menu Ordinary Co Kriging Menu Return To Main Menu Set Program Parameters Cross Validation Ordinary Co Kriging Line Contour Diagram Block Contour Diagram Statistics Menu Variogram Menu Disjunctive Co Kriging Menu user menu If the highlighted key 0 is typed or the light bar placed over the menu option Ordinary Co Kriging Menu on the MAIN Menu and th nter key pressed th Kriging Menu is activated giving access to several programs for calculating
77. s in GEOPACK read the DEFAULT file to obtain the name of the data set The first part of the data set name i e TEST for a data set named TEST DAT is used for many of the intermediate file names For a data set named TEST DAT which is assumed to contain three variables moist variable 1 temp variable 2 and sand variable 3 the typical file names that reside in the temporary storage directory and a brief description of their purpose follows STACKER Used by the menu program MENUTEMP BAT Used by the menu program DEFAULT Contains the name of the data set and path of origination EST DAT Data set EST STS Basic descriptive statistics for all data variables in the data set RPLOT TMP Temporary file containing the data for the last regression or least squares graph GRAPH DEF A command file for the graphics program Contains the commands used to generate the last graph regression least squares contour plot etc TEST V The default settings file for the semivariogram program This file is generated when the Default Settings program on the variogram menu is executed VPLOT DEF VAR11 00 VAR11 01 VAR12 00 VAR11 00 MVAR11 01 MVAR12 00 TEST VAR KPLOT TMP KPLOT1 IMP TEST DCi DPLOT TMP DPLOT1 IMP Temporary file containing the data
78. s program allows you to see a diagram of all the sub directories that branch off the current or specified subdirectory To use type SHOWDIR lt any dir gt This program allows you to alter the system settings for the parameters listed under EVOKE To use this program type DEFLT SYSETUP SYSDEFLT 43 3 1 VIRUS DI ECAY RATI Description of Data viruses wer temperature added determin th The samples were At predetermined times SECTION 3 EXAMPLES ES IN TUCSON GROUND WATER Water samples were obtained from 71 continuously pumping public water supply wells in the Tucson Basin The water samples were taken to the laboratory and incubated at the in situ ground water subsamples were withdrawn and assayed to number of virus particles remaining in the water The decay rate was calculated as the slope of the line drawn through the data using linear regression and has the units of log virus particles day Geostatistical Calculations requirements and is included in the directory G The data set was configured in the following way according to GEOPACK VIRUS DAT Ground Water Data for the Tucson Basin 2 71 500 00 1 2 3 4 TEMP DECAY 5 0 4F10 3 1 8 498 7 2 14 129 6 3 14 330 8 4 5 280 8 5 5 079 8 6 6 084 Ji 7 7 291 6 8 5 883 5 9 17 951 6 10 2 263 8 11 0s TST 9 12 5 280 7 13 6 285 6 14 8071 7 15 14 9
79. s to create a grid system with estimated values and estimation variances at each of the nodal points To do this you must supply the following information 1 The origin of the grid system usually the origin for the collected data is used 2 The number of columns of estimates in the X direction 3 The distance between columns in the X direction 4 The number of rows of estimates in the Y direction 5 The distance between rows in the Y direction For this case the total number of estimates is Number of columns Number of rows Read Locations From a File An alternative method for determining the placement for calculating estimates is to create a file which contains a list of the desired X and Y coordinates for the placement of the estimates When using this option GEOPACK will prompt you for the file name and use the file to determine the placement of estimates Line Contour Diagram A contouring package is provided with GEOPACK so that the output files from the kriging program can be graphically illustrated The output file from the kriging program is in the temporary storage directory with a name KPLOT TMP The contouring program reads this file and produces an output file KPLOT1 TMP which can be used by the graphics program to draw a contour plot on any device for which a device driver is supplied Block Contour Diagram The pixel contour program is similar to the line contouring program described above
80. tallation instructions exe b Temporary storage directory Ge Ae c Setting or changing the GEOPACK directory specification 5 pom i d GEOPACK System hetanlt Sab ings 3 System Overview a Program structure tS tee i b Function keys and cursor no remione c File naming conventions 4 Data File a Format instructions b Examples of Data Sets 5 The Menu System a Description of the MAIN Menu Smet ud b Description of the HELP Menu F1 c Description of the UTILITY Menu F3 d Description of the VIEW Feature F4 e Description of the USER Menu F5 f Description of the Data Set Utility Menu g Description of the Statistics Menu h Description of the Variogram Menu i Description of the Kriging Menu E ee j Description of the Disjunctive Kriging Menu k Modifying and Adding Menus 1 Trouble shooting 6 GEOPACK Enhancements a Running GEO EAS geostatistics software b Description of GEOPACK utility programs 3 Examples 1 Virus Decay Rates In Tucson Ground Water 2 Salinity In a Southwest Arizona Field 3 Surface Moisture Temperature and Texture References and Suggested Literature N p ol U w Q oO Ea H ES Olsa tw oe CG Cel A jpa A NO Do Oy Slalors BBERREES LIST OF FIGURI Gl ioe Figure 3 1 1 Example output from Variogram Calculation Sample program for the data set VIRUS DAT In A and B respectively are the tabular values and a plot of t
81. te the 00th or Olth specified random function s such as for a direct semivariogram for MOIST for a cross semivariogram for MOIST and 00 01 02 03 etc saved sample semivariogram for the Given in Section 2 3 is a description of the naming convention used by GEOPACK The numbers i e 00 or 01 etc are the extension of the sample semivariogram file name Typin the fittin variogram file that the cursor is hi to help you determine which file yo g RETURN selects the par g program from which i e VARij 00 ticular sample semivariogram file for use by Typing F1 gives some information about the sample semi ghlighting This help information is supplied u want to use when you have a number of files to choose The output from the fitting program is stored on the temporary drive or semivariograms saved SEE SECT After a sample sen subdirectory using a naming convention similar to the sample ON ABOVE ON SAVING coefficients are saved in a file lt RAM drive gt mVARij 00 first saved coefficient lt RAM gt VARij lt RAM drive gt mVARij 01 second file lt RAM drive gt mVARij 02 lt RAM drive gt mVARij 14 nivariogram has been modeled and the results THE SAMPLE SEMIVARIOGRAM the model semivariogram model file This file corresponds to 00 saved third file saved fifteenth file saved where the m is used to designat
82. the data set ECSAR DAT 57 Figure 3 2 2 conductivity using the Disjunctive pam Level 0 1894 6 6179 Level 2 8 6179 E 0 926 Level 3 8 826 lt 1 049 evel 4 1 849 1 229 evel 1 229 lt 1 347 evel 6 1 347 1 431 evel 1 491 1 752 evel 9 1 752 2 636 Contour diagram of the estimated value of 58 File DPLOT THP the electrical Co Kriging and Block Contour Diagram programs File Data View 8 2cut 1 38 File OPLOT TMP ees EEn N 1 2 3 4 5 6 8 Figure 3 2 3 Contour diagram of the conditional probability that the estimated value of the electrical conductivity is greater than the natural logarithm of 4 dS m i e 1 38 log dS m using the Disjunctive Co Kriging and Block Contour Diagram programs This figure shows the actual screen position of the contour levels window when displayed 59 EMPERATURE AND SOIL TEXTURE T H 3 3 SURFACE MOISTURE Description of Data This data set contains three random functions the surface moisture content 9 the surface soil temperature T and the sand content of the surface 1 cm The moisture content and sand content data were collected at 71 random locations and the temperature data at 120 random locations on a lm by lm grid system in a 1 ha field at the Campbell Agricultural Center of the University of Arizona A more detailed description of the data and techniques used to measure the EC an
83. this is done the computer may stop operating since there is insufficient memory to contain both the current and pre installed versions of GEOPACK Execute an MS DOS Command This Utility is similar to DOS Shell except that it allows you to run ONE MS DOS command Once you have run the MS DOS command you are returned to the Utility Menu If you need to run several MS DOS commands it is more efficient to exit to a DOS shell Please Note There is slightly LESS available computer memory when Executing an MS DOS command compared to exiting to a DOS shell Graph Most Recent Graphic This convenience feature allows you to replot the last graph displayed or that should have been displayed on the screen This feature is useful for computers with insufficient memory to display graphs while in an application program i e the computer doesn t have enough extra memory to run the graphics program Use this options if you don t see 4g graph and receive th rror message OUT OF MEMORY Program Structure This Utility gives a pictorial representation of the current GEOPACK structure for an example s Section 2 3 a Changes in the structure of GEOPACK will be reflected in the diagram produced by this program The USER menu described in Section 2 5 d can be modified to include any program or add another menu In the abov xample the USER menu is used to access four other menus
84. ting procedure is used and yields yCh 0 27 0 66 1 5h 145 0 5 h 145 J O0 lt h lt 145 5 yh 0 93 y h gt 145 and is shown in Figure 3 2 1 This variogram model was used in the cross validation procedure listed on the Ordinary Co Kriging Menu which attempts to fit both the sample semi variogram and the reduced mean and variance simultaneously An acceptable model variogram is given when the reduced mean and variance are approximately 0 0 and 1 0 respectively subject to a reasonable fit to the original sample semivariogram Using the Cross Validation procedure on the Ordinary Co Kriging Menu the reduced mean and variance of the above model can be determined and are respectively 0198 and 1 224 The cross validated model is somewhat different from the one listed above because now the fitting procedure also tries to fit the reduced mean and variance For this case the semi variogram model is y h 0 36 0 52 1 5h 153 0 5 h 153 J O0 lt h lt 153 51 yh 0 88 y h gt 153 55 For the model given above the reduced mean and variance respectively wer 0 0241 and 1 062 One problem in using the reduced mean and variance for determining the adequacy of semivariograms is that there is no independent method for determining how close to zero and unity the reduced mean and variance should be and therefore using this technique to fit models to a variogram is somewhat subjective Viewing the two
85. to hold information such as the data set intermediate results output files etc The installation procedure automatically creates a temporary directory called TMP to be used to store intermediate results In general the temporary storage directory is transparent to the user 22s Setting or Changing the GEOPACK Directory Specification GEOPACK will operate properly only if the environment variable SGEODIR the are used to indicate an environment variable is set to the root of the geostatistical programs To set this variable the following line should be added to the AUTOEXEC BAT file Ne nw SET GEODIR C GEOPACK where C GEOPACK is the primary subdirectory for the geostatistical programs In the user defined menus described in Section 2 5 d whenever GEOPACK sees S GEODIRS it will substitute C GEOPACK so that a command GEODIR SHOWDIR would be the same as C GEOPACK SHOWDIR Note the above command can also be typed at the MS DOS prompt prior to starting GEOPACK After typing the SET command given above if the DOS reply Out Of Environment Space appears the user should consult the DOS manual about SHELL commands 2 2 e GEOPACK System Default Settings The installation program creates a file that contains the system default settings This file may require modification before all of the options on the USER and other menus become active
86. to various files while running GEO EAS since it doesn t have a specified naming convention When GEOPACK writes a file which is in GEO EAS format it always has the extension EPA i e lt name gt EPA GEOPACK will save up to 15 sample semivariograms using the following naming convention lt RAM drive gt VARij 00 first saved sample semivariogram for variable i with j i j l I1VAR if variable 1 is MOIST 2 is TEMP and 3 is SAND then if i l and j 2 VARij 00 is the first cross variogram between MOIST and TEMP saved by GEOPACK 26 lt RAM drive gt VARij 01 second saved sample semivariogram CRAM drive gt VARij 02 third saved sample semivariogram 03 lt RAM drive gt VARij 14 fifteenth saved sample semivariogram Set Program Parameters GEOPACK provides you with a program for setting the variogram parameters to facilitate using GEOPACK in an efficient manner This program allows you to specify a value for any of the parameters used to calculate the sample semi variogram or cross semivariogram You can specify any or all of these parameters and once they are specified the program will not ask for interactive input during execution For example if you want to run the program five times and are planning to change only one parameter each time you would give a in the parameter
87. urface graphics text editing and data base management systems The program names are defined in the GEOPACK System Default Settings file see Section 2 5 c Other miscellaneous user defined programs can also be incorporated into GEOPACK using the USER s Menu see Section 2 5 e Basic Statistics Basic statistics such as the mean median variance standard deviation skew kurtosis and maximum and minimum values can be determined for the selected data base i e a file containing one or more random functions plus their x and y coordinates Programs are also included for linear regression polynomial regression Kolomogorov Smirnov test for distribution and calculating several percentiles of a selected data set i e for a particular random function such as moisture content GEOPACK can also directly access any commercially available statistics package while running GEOPACK which allows the user to run more comprehensive statistical analyses contained in a commercially available statistics package Variography The sample semivariogram the cross semivariogram or a semivariogram for combined random functions i e Z x Y x for a two dimensional spatially dependent random function can be determined The approach used in determining the sample semivariogram is similar to that outlined in Journal and Huijbregts 1978 A model can be fitted to the sample semivariogram using the nonlinear least squares fitting pro
88. ut to the screen as Percent Completion on the lower right hand side 13 Both a table of values and a plot of the sample variogram are printed to the screen For this data set the output appears as shown in Figure 3 1 1 Note the following figures use the device drivers supplied with GEOPACK Publication quality figures can be created using an appropriate graphics package and the USERS MENU F5 14 You are now given several options Select Options to add labels to your graph Upon Exiting this menu you are returned to the Variogram Menu 15 Select Automatic Model Fit 16 You will again be asked several questions then allowed to choose the autocorrelation function you wish to model 17 Select a model type in this case D spherical The input parameters are printed to the screen as well as the input data If you wish to delete any of the data type D Enter the Observation number and Enter You need to repeat this step for each line you want to delete In this case we delete lines 8 through 12 18 Several screens will be printed detailing the results of the model variogram calculations The model fit to the data will then be printed to the screen For this example the output is as shown in Figure 3 1 2 19 Once again you are given the opportunity to add labels etc to the graph 20 Upon Exiting the screen you are asked if you want to rerun the program If No you are returned to the Var
89. variograms using the Fit Models Manually option on the Variogram Menu it appears that the neither of the models produces an adequate fit for both the sample semivariogram and reduced mean and variance For this reason an alternative model is chosen that falls in between the cases listed above This model is y h 0 30 0 60 1 5h 160 0 5 h 160 0 lt h lt 160 5 y h 0 90 y h gt 160 and has a reduced mean and variance respectively of 0 0203 and 1 19 Step 4 Calculate the Hermite Coefficients The next step in the disjunctive kriging process is to find the coefficients which define the Hermite transform function See Theory of Geostatistics listing on the GEOPACK User s Manual Type Fl To obtain the Hermite coefficients it is necessary to select the Hermite Coefficients listing on the Disjunctive Kriging Menu There are a number of questions that must be answered during the execution of this program These questions will appear only if the Set Program Parameter program was not run prior to this selection Step 5 Create a Grid of Estimates Using Disjunctive Kriging A total of 2500 estimates of EC and In EC using each method were obtained on a 5 by 5 meter grid system superimposed over the field sampled by Al Sanabani 1982 Along with each estimate a value of the kriging variance was calculated and for the disjunctive kriging method a value of the conditional probability Bower and Wilcox 1965
90. you may type J to jump ahead The results of the Kolomogorov Smirnov Test for Distribution are output to the screen In this case we accept the null hypothesis at the 0 05 level and thus there is some evidence that the data are normally distributed If the data were not normally distributed it would be possible to transform the data into a new data set with a normal distribution A logarithmic transformation is a common technique for transforming data into a normal distribution You are returned to the Statistics Menu Step 3 Determining the Variogram Next the sample spatial correlation structure i e the sample semi variogram must be determined Without this functional relationship between the distance and the variance it is not possible to use the kriging techniques 7 Select Variogram Menu 8 Select Variogram Calculation Sample 9 Select type of correlation function in this case A semivariogram 46 10 Selectthe principal function in this case B decay 11 You will now be asked several questions about how you want the calculations performed unless you have set up the default settings file in such a manner as to avoid this When responding to the questions you may either type in a number or push Enter to select the default value which is shown on the lower left hand side of the screen 12 After all of these questions have been answered the variogram is calculated The progress of the calculations is outp

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