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1. GRAPH OPTIONS Axes Parameters Tick Parameters Axis Style Full x Graph Limits Base i Auto x Y Type Auto Min 254 400 118 000 Label Auto Max 492 000 315 000 Fraction Auto Exponent Auto Titles Labels Main title Postplot of Cadmium from data file Example dat Subtitles KX Label Easting feet Y Label Northing feet Tick Parameters Graph Limits Title Labels Reset Quit Select style for X and Y axes Figure 13 3 Postplot Graph Options Screen The Graph Options screen and menu displayed in Figure 13 3 provides control over the graph background parameters These parameters are used to specify the axis style the graph limits titles and axis labels and the tickmark labeling and spacing The menu line appears as follows Axis Parameters Tick Parameters Graph Limits Title Labels Reset Quit Axis Parameters The Axis Parameters option allows the selection of the type of axis style for the background of the plot The screen field accessed from this option is a toggle field Choices avalable are Half left and bottom axes only Full left right top and bottom axes and Grid the same as Full but the maja tickmarks extend across to the opposite axis The default axis style is Full Tick Parameters The Tick Parameters option allows specification of the nature of the numerictickmark labels to be placed along each axis This is accomplished with a set of closely inter related parameters which cont
2. Data File C NGeoEASNData Exanple dat Variable Cadmium Lower Limit 000 Upper Limit 16 700 Absolute Axes Class Limits Minimum Maximum Minimum i Class Width Tic Spacing Classes Main Title Histogram sub Title Data file Example dat K Axis Cadmium ppm Y Axis Frequency Type Class Limits Axes Titles Results Quit View the histogram as a graph Figure 7 6 Statl Histogram Options Screen The Histogram Options screen and menu Figure 7 6 provides the options necessary to generate a histogram frequency distribution plot of the data You can examine the histogram results or view the graph A histogram is displayed before the Histogram menu is accessed Pressing any key will access the Histogram menu from the histogram display The histogram plot is discussed below in the View Graph option of the Histogram menu The menu line appears as follows Type Class Limits Axes Titles Results View Graph Quit Type The Type option is used to select the Frequency type The Frequency type is selected from a two valued toggle field containing the choices Absolute and Relative The choice Absolute will generate a traditional histogram Relative will cause the frequencies to be displayed asa percentage of the total number of samples or weight of the samples retained Class Limits The Class Limits option allows the specification of the class upper and lower limits You will be prompted for the minimu
3. Minimum Maximum Prefix Data Variable Limits Batch Statistics Quit Compute basic descriptive stats Figure 7 1 Stat Main Screen The main menu and screen Figure 7 1 has options to allow specification of the data file names the selection of the variable to be used the selection of upper and lower limits for the variable calculation of statistics univariate and generation of a batch statistics report The menu lire appears as follows Prefix Data Variable Limits Execute Batch Statistics Quit Prefix The prefix option is used to enter the prefix for the data file name Data The Data option is used to enter the name of a Geo EAS data file Variable The variable option allows the selection of a variable for which univariate statistics are to be generated The weighting factor variable can be selected at this time The choices available for variables are the variable names specified in the data file The natural log transform may be chosen to compute log statistics Both the weight and log parameters may be used simultaneously The screen fields accessed from this option are Variable A toggle field for selecting the variable name whose values are to be used to compute the univariate statistics The default value is the first variable in the data set Weight A toggle field for selecting an optional variable name whose values are to be used as the weighting factor If the weighting factor variable is chosen then the re
4. See the section on the Lag Results menu below for more information Model The Model option provides access to the Model screen and menu See the section on the Modeling menu below for more information 10 7 THE LAG RESULTS MENU LAG RESULTS Min Distance GT Lag Number Max Distance LE Number of Pairs Average Distance All data Lag data From pairs To pairs Mean S 7 885 8 206 6 286 6 206 Variance 15 273 14 131 14 131 14 131 Spatial correlation estimators Statistics for difference Z Variogram i Minimum 000 Relative Vario x 25th Z L1l6 1 690 Madogram c Median i 16 000 InuCouv Vario 2 Mean 31 668 75th tile 43 560 Maximum 3 249 640 Scatter Examine Write Quit Generate a Lag Histogram Figure 10 7 Vario Lag Results Screen The Lag Results screen and menu has options to alow you to view detailed results for a specific lag The menu line appears as follows Histogram Scatter Examine Write Quit Histogram The Histogram option allows you to view a lag histogram plot Thebars on the histogram represent the number of squared differences increments Z x Z x h in each histogram class A box plot is appears at the top of the graph to display the frequency distribution of the entire set of differences The variable name is displayed in the title of the graph Vertical and horizontal axes scaling and the tick mark spacing are calculated automatically by the program Displayed on the right side o
5. estimate Conversely if a cell center is outside and inclusive or inside an exclusive polygon the flag is set to exclude computation of an estimate at that location The rule which governs processing of multiple polygons is this No flag may be changed to include an estimate which has been Excluded by a previous polygon for additional information see the Polygon option of Section 12 Polygon files may contain an unlimited number of polygons The first record line in the file should contain the number of polygons contained in the file Each polygon may be specified as an inclusive Code 0 or exclusive Code 1 polygon A polygon is specified by placing a polygon header record in the file followed by no more than 100 polygon vertex records A polygon header record consists of two integers The Include Exclude Code 0 or 1 followed by a comma and the number of vertices lt Nv gt in the polygon Exactly lt Nv gt vertex records must follow Each vertex record consists of two floating point REAL numbers separated by acomma These should be listed in an order such that straight lines connecting successive vertices would form a closed polygonal boundary if a final line were drawn from the last vertex to the first Polygon files may be created by any simple text editor such as the DOS editor EDLIN or any word processor using non document mode All lines in the file must be terminated with a CRLF carriage return line feed B
6. the file specified Scale Factor 10 0 Decimals gt 4 Include Symbols 4 Prefix Data Variables Options Graph Options Quit Generate the plot Figure 13 1 Postplot Main Screen Prefix The Prefix option is used to enter the prefix for file names Data The Data option is used to enter the name of a Geo Eas data file Variables The Variables option allows the selection of variables that are to be used as the X and Y coordinate values and the sample values to post The choices available are the variable names as specified in the data file The screen fields accessed from this option are X Coordinate Variable A toggle field for selecting the variable name whose values will be used as the X coordinates The default X variable is the first variable in the data file Y Coordinate Variable Variable to post Options A toggle field for selecting the variable whose values will be used as the Y coordinates The default Y variable is the second variable in the data file A toggle field for selecting the variable whose values will be posted on the plot The default variable to post is the third variable in the data file The Options option allows the specification of how the sample locations are to be marked on the graph The screen fields accessed from this option are Include Values Size Scale Factor Decimals Include Symbols A two valued Yes No toggle field to enable or disable the labeling of samples with th
7. Execute Quit Files Execute Quit Files Variables Execute Quit Files Variable Execute Quit 5 4 THE MAIN MENU DATA PREPARATION 1 2 1 Data File Prefix C NGeoEASSDatas Scratch File Pref ix DESCRIPTION This option displays file operations along with a narrative describing each choice These operations are append column variable extract row extract compress ID var merge report and sort These operations can produce output files with a maximum of 48 variables and 10 000 records If you wish to use one of these operations or require more information on a specific operation then press lt enter gt Prefix DOS Utilities BRR east Quit Figure 5 1 Dataprep Main Screen The Main screen and menu Figure 5 1 provides options which allow you to access the DOS Utilities and File Operations menus The menu line appears as follows Prefix DOS Utilities File Operations Quit Prefix The Prefix option is used to enter the prefix strings for the data file and the scratch file DOS Utilities The DOS Utilities option provides access to the DOS Utilities menu The DOS Utilities menu provides access to the DOS commands such as Duectory Print List same as the DOS MORE command Copy Rename and Delete Refer to your DOS manual for further information on these DOS commands The DOS Utilities menu is discussed below File Operations The File Operations option provides access to the File Operatio
8. The menu line appears as follows Error Map Scatter Plot Histogram Write Examine Quit Error Map The Error Map option provides a graph of the kriging error or Differences An example plot is displayed in Figure 11 6 Sample locations are marked with a symbol for over estimation Estimate Observed gt 0 and an x symbol for negative differences The size of the symbol is proportional to the error so that large positive or negative differences are easily noticed Descriptive statistics for the differences are displayed to the right of the graph Plot of Error 2 Cadmium Statisti N Total N Miss N Used Mean Std Dev S E H D Minimum 25th z Median Toth z Max imum Figure 11 6 Xvalid Error Map Scatter Plot The Scatter Plot option provides a choice of displaying one of two possible scatter plots When this option is chosen a two valued toggle field containing the choices Observed vs Estimate and Estimate vs Error is displayed on the message line It is used to select the type of scatter plot to be displayed Once this choice has been made the appropriate graph will be displayed Box plots are drawn opposite to each coordinate axis to convey information about the frequency distributions of the observed values and estimates or estimates and differences In both types of graph and x symbols are used to indicate positive and negative estimation errors same as the Er
9. compatible printers Type the command HPPS before executing any Geo EAS programs and you can then use the lt Print Scrn gt key to obtain hardcopy of any Geo EAS graphic Alternate options far obtaining hardcopy include screen capture utilities which are now part of many word processing packages such as WordPerfect 5 1 or stand alone screen capture programs such as InSet These provide device drivers for a variety of printers Is there a way to plot variograms histograms and probability plots on my pen plotter No Geo EAS only provides plotter support for metacode files produced by three programs POSTPLOT XYGRAPH and CONREC How do I create my own Geo EAS file Geo EAS does not provide any data entry or editing capability Use your favorite text editor or word processor Retrieve an existing data file and edit it to match the Geo EAS format or type in the file from scratch Geo EAS files contain several lines of header information followed by a data table The basic rules are The first line is a title The second line contains the number up to 48 of variables columns The next n lines one per variable each contain the variable name and optionally unit and format information The data table must contain one row per observation usually up to 1000 The data table must contain only numbers in integer decimal or exponential e g 5 6E6 format separated by blanks or commas Variable columns need not be align
10. for entering the title of the graph The default title is the title from the data file Three alphanumeric fields which may contain up to 60 characters each for entering the graph subtitles The default for the first subtitle is the name of the contour variable An alphanumeric field which may contain upto 60 characters for entering the X axis label The default X axis label is the X coordinate variabk name An alphanumeric field which may contain upto 60 characters for entering the Y axis label The default Y axis label is the Y coordinate variabke name Six toggle fields for selecting the character size for the labels The choices available are 0 to 10 where 0 is the smallest and 10 is the largest character size The default for the Main Title is 6 The default for the first and second subtitles and the X and Y axes is 5 The default for the third subtitle is 4 These choices work well on the screen however smaller sizes might be more suitable for output to a plotter Annotation The Annotation option allows the user to suppress the axes titles and labels for the graph The screen field accessed from this option is a toggle field that is displayed on the message line The choices available are Plot axes and titles or No annotation do not plot axes and titles The default is Plot axes and titles 15 7 THE CONTOUR OPTIONS MENU ontour Options Spline Tension 15 8 Contour Level Label 00000E 66 10000E 66
11. indicating that the range is too low It appears that the curve would fit well if it were shifted about 25 to the right so you should try again with a range of 100 OPTION ACTION FIELD VALUE MODEL Accept Nugget 5 Accept Type Spherical Accept Sill 11 Input Range 100 PLOT lt Q gt The resulting graph is displayed in Figure 4 12 Variogram for Cadmium Parameters File Examp le pct Pairs 1366 Direct HAB Tol H ABA MaxBand ma E H n D H gt Cadmium Limits Minimum Maximum Mean Var 80 Distance Figure 4 12 Variogram model Nugget 5 Spherical Sill 11 Range 100 This is an excellent fit about as good as you can get with a spherical model That low fifth point however suggests that an exponential model which has a more gentle airvature may also provide a good fit If you are unfamiliar with the four types of models available in VARIO repeat the option sequence above three more times changing the model type each time A bit of trial and error leads to an exponential model with a nugget of 4 5 sill of 13 5 and range of 160 Ths graph is displayed in Figure 4 13 OPTION ACTION FIELD VALUE MODEL Input Nugget 4 5 Toggle Type Exponential Input Sill 13 5 Input Range 160 PLOT lt Q gt Some obvious questions that come up at this point are Which one of these models is best How do you decide which one to use What happens if you pick the wrong one Unfortunately ther
12. the shape is typical of a spherical model variogram i e an initial linear increase from the Y intercept curving relatively sharply into a horizontal constant value The spherical type of variogram is observed frequently in experimental variograms and is one of the model options available in Geo EAS To fit a spherical model to a variogram you need to estimate the nugget or Y intercept the sill or difference between the nugget and the maximum value and the range or distance at which the model reaches the maximum value With a little practice good fits can usually be obtained within two or three tries Try an initial model with a nugget of 5 a sill of 11 and a range of 80 using the following option sequence Note that after variogram model parameters have been entered the lt Left gt arrow key 1388 HHA 668 nea can be used to exit the model option The resulting graph is displayed in Figure 4 11 OPTION ACTION FIELD VALUE MODEL MODEL Input Nugget 5 Toggle Type Spherical Input Sill 11 Input Range 80 PLOT lt Q gt Variogram for Cadmium Parameters File Examp le pct Pairs 1366 Direct HBA Tol AAA MaxBand na E N S D H m gt Cadmium Limits Minimum Maximum Mean Var 80 Distance Figure 4 11 Variogram with model Nugget 5 Spherical Sill 11 Range 80 This model fits reasonably well at the nugget and sill but the initial slope is too steep
13. 1 2 1 A preprocessor for program VARIO File Prefix C GeoEASSData Files Variables 5 Data File Example dat Records 60 Pair Comparison File Example pcf Pairs possible 1770 Max 16384 Variables Fraction 1 000 Seed 1951 X Variable Easting Y Variable Northing Execute Minimum Maximum Select this option to build the X 254 400 492 000 pair comparison file Distances T 118 000 315 000 and directions for all pairs will Distance 000 308 647 be computed sorted and saved Frefix Files Variables Limits Subset Quit Build the pair comparison file Figure 4 7 Prevar Main Screen Tthe random seed may be different in what you actually observe on your screen Select the subset option and change the seed to 1951 The option sequence below creates the par comparison file Example pcf OPTION ACTION FIELD VALUE FILES Accept Data File Example dat Accept Pairs File Example pcf EXECUTE Next initiate Vario and the Vario Main screen is displayed as in Figure 4 8 VARIO 1 2 1 A program for computing var iograms File Pref ix C GeoEAS Data File Vars 5 Kept l 64 Data 66 Obs lt 4 2 Pair Comparison File Example pcf Pairs 1776 Missing H Variable Variable Cadmium Variogram Options Log Option Off Use this option to display the Variogram Options Screen and menu Limits Variogram options may be selected Minimum and the variogram may be computed Maximum Prefix Data Variable Limits H
14. 2153 X Variable Easting Y Variable Northing Execute Limits Minimum Maximum select this option to build the X 254 400 492 000 pair comparison file Distances Y 118 000 315 000 and directions for all pairs will Distance 000 308 647 be computed sorted and saved Frefix Files Variables Limits Subset Quit Build the pair comparison file Figure 9 1 Prevar Main Screen The Main screen and Figure 9 1 menu has the options to allow specification of the input data and the pair comparison file names the selection of the variables to be used and the limits m sample coordinates and the interpair distances The menu line appears as follows Prefix Files Variables Limits Execute Quit Prefix The Prefix option is used to enter the prefix for file names Files The Files option is used to enter the input data and the pair comparison file names The screen fields accessed from this option are Data File An alphanumeric field that may be up to 14 characters used for entering the name of a Geo EAS data file Pair Comparison File An alphanumeric held hat may be up to 14 characters used to specify the name of the pair comparison file This file will contain the contents of the input data file and the information for each pair of samples the distance between the two sample points and their relative direction The default Pair Comparison File is the name of the data file with a pd extension For example if the Data File is Exampl
15. 3 the flag settings are REVERSED for blocks OUTSIDE the current polygon Blocks inside remain unchanged The new Sample Select option can be set to YES or NO resulting in operation as follows IF Sample Select NO the default the polygon option operates only on points or blocks to be kriged dl samples in the data file are used fo Kriging IF Sample Select YES the polygon option operates on bothe the points or blocks to be Kriged AND on the samples Only samples winthin areas flagged INCLUDE are used for kriging The polygon file is read when the Execute option is used to initiate kriging If an error occurs while reading the Polygon file a message will be generated the file will be ignored and a attempt to krige all grid cells will be made See the appendices for a detailed description of the polygon file format Type The Type option is used to select the type of kriging to use and whether to krige point or block estimates The screen fields accessed from this option are Type of Kriging A toggle field containing the choices Ordinary and Simple which is used to specify the type of kriging to perform If Ordinary is chosen ordinary kriging will be performed If Simple kriging is chosen simple kriging is performed and a value must te specified for the Global Mean when entering the variogram model parameters on the Variables Models screen Point or Block A toggle field containing the choices Point Block 2x2 Block
16. 4 ERROR AND RECOVERY PROCEDURES 0 000005 25 4 1 OVERVIEW cee oo 2 och pee hah oath See Bere eee Bees Seek ea ee ee Sees 27 4 2 EXPLORATORY DATA ANALYSIS 0 000000 eee eee 27 4 3 VARIOGRAM ANALYSIS 0 2 ene 35 4 4 KRIGING AND CONTOURING errereen 49 4 5 SUMMARY AND EXERCISES erneer 55 SECTION 5 DATAPREP 5 1 WHAT DATAPREP DOES 0 0000 eens 57 SECTION 6 TRANS 6 TRANS 6 1 WHAT TRANS DOES KR RRR eee eee eens 72 Geo EAS 1 2 1 iii Table of Contents Table of Contents CON T 7 1 WHAT STATI DOES s K KR re bri PEro mE TaVo ra tE ERPE TETE GNE 81 SECTION 8 SCATTER 8 1 WHAT SCATTER DOES lt 74 R RR ties IA ETRE RR nep neia egi 93 SECTION 9 PREVAR 9 1 WHAT PREVAR DOES x gg RRR R RRR R KR RRR R eae 96 ECTION 10 VARIO 10 1 WHAT VARIO DOES 0 0 ce eee 100 ECTION 11 XVALID 11 1 WHAT XVALID DOES 0 0 ee eee 116 SECTION 12 KRIGE 12 1 WHAT KRIGE DOES 65 5 RTE ee 0d eed epee ee eA Wee heed Spe ened T 130 ECTION 13 POSTPLOT 13 1 WHAT POSTPLOT DOES 0 S R 2h thes eben dwar R RT obs 145 ECTION 14 XYGRAPH 14 1 WHAT XYGRAPH DOES 0 0 00 cece 153 SECTION 15 CONREC 15 1 WHAT CONREC DOES enen eene eee ee ee eee ee 162 16 1 WHAT VIEW DOES 20 ep t ERTE HE ee tee nee 172 SECTION 17 HPPLOT 17 1 WHAT HPPLOT DOES ini iches T KET E ERE ERT eee 174 APPENDICES APP
17. 426 Direct HBA Tol H 22 588 MaxBand na Cadmium Limits Minimum Maximum Mean Var Variogram for Cadmium Parameters File Examp le pct Pairs Direct Tol S MaxBand Cadmium Limits Minimum Maximum Mean Var 80 126 Distance Figure 4 17 Variogram Exponential Model Direction 45 358 4666 508 nma Variogram for Cadmium Parameters File Examp le pct Pairs Direct Tol MaxBand Cadmium Limits Minimum Maximum Mean Var 80 126 Distance Figure 4 18 Variogram Exponential Model Direction 90 344 4668 506 nia Variogram for Cadmium Parameters File Examp le pct Pairs 348 Direct HHA Tol 506 MaxBand nma E N S D H gt Cadmium Limits Minimum Maximum Mean Var 80 126 Distance Figure 4 19 Variogram Exponential Model Direction 135 These four variograms provide a good illustration of why you usually model the omnidirectional variogram first In the directional variograms most of the definition of shape nugget and sill has been obscured You can see however a general confirmation of the assumption about the anisotropy The points on the 0 degree variogram all fall below the omnidirectional model suggesting the range in that direction should be longer The opposite is true for the 90 degree variogram while the 45 and 135 degree variograms are reasonably well fit
18. 8 1 Scatter Main Screen Data The Data option is used to enter the name of a Geo Eas data file Variables The Variables option allows the selection of variables that are to be used as the X and Y coordinate values and the sample values to post The choices available are the variable names as specified in the data file The screen fields accessed from this option are X Variable A toggle field for selecting the variable name whose values will be used as the X coordinates The default X Variable is the first variable in the data file Y Variable A toggle field for selecting the variable name whose values will be used as the Y coordinates The default Y Variable is the second variable in the data file Log Two two valued toggle fields to enable or disable a logarithmic transformation of theX and or Y coordinate values The choices available ate On use logarithmic scaling and Off If the log option is set and the number of missing data data values less than zero or the missing value is equal to the number of data records an error message is displayed The default value is Off Options The Options option allows selection of linear regression and a scaling option The screen fields accessed from this option are Regression A two valued Yes No toggle field to enable or disable the calculation of a regression line The regression line and the coefficients are plotted on the graph The coefficients are the slope and interc
19. D0000E 48 1Z090E 81 1664HE H1 CBBHBE 41 246HHE 81 Starting Contour Value Maximum Contour Value Contour Level Increment Contour Levels Labeling Option Label Skip Factor First Level to Label Label Size WO Co J C OF d L N KA Dash Pattern Dash Cutoff Rep Label Annotation Option Plot Min Max Character Size 8 New Levels Edit Levels Labeling Dash Pattern Spline Quit Select graph annotation options Figure 15 5 Conrec Contour Options Screen The Contour Options screen and menu Figure 15 5 has options to allow specification of the contour levels labels the skip factor label size and the selection of a dashed line pattern The menu line appears as follows New Levels Edit Levels Labeling Dash Pattern Annotation Spline Quit New Levels The New Levels options allow you create a list of equally spaced contour values and labels The defaults for these screen fields may be calculated by the program when the Variables option is selected The program calculates the contour levels and the corresponding labels based on the values from these fields The screen fields accessed from this option are Starting Contour Value A numeric field for entering the lowest contour level Maximum Contour Value A numeric field for entering the highest contour level Contour Level Increment A numeric field for entering the increment value between the contour levels Edit Levels The Edit Levels option allow you to cha
20. Entitonmenial Megs Bore Font O07 Geostatistical Environmental Assessment Software Underlining Geostatistical Environmental Assessment Software Special characters from font 010 and font 008 Special Characters 3 1 euperscripting using the gt character Easting meZ Easting m APPENDIX D POLYGON FILE FORMAT This section describes the format of a polygon file They are used by program KRIGE to include or exclude computation of estimates within specified polygon areas Polygon files are text files comprised of lists of X Y coordinate pairs vertices which form closed polygonal boundaries These boundaries may be defined as inclusive or exclusive meaning that estimates should be excluded outside of inclusive boundaries and included when outside of exclusive boundaries The polygon file is processed in the following manner Krige reads the specified polygon file before kriging and builds a matrix of flags to indicate if point or block estimates are to be included or excluded This matrix corresponds to the grid defined be the user in the Krige Options Screen Polygon files must be constructed with these grid boundaries in mind because the grid and polygon boundaries are related As krige reads each polygon from the polygon file each grid cell center is tested If the cell center point or block center is inside an inclusive polygon or outside an exclusive one the corresponding flag is set to include the
21. Examine Screen The boxplot Figure 7 4 is a graph which depicts the limits quartiles median and mean of a set of values Boxplots are used in the Probability Plot and Histogram displays A Boxplot R comprised of a rectangle containing an X and a dividing line A lineextends outward from each end of the rectangle The rectangle represents the interquartile range the range of values between the Ist and 3rd quartiles The dividing line marks the position of the median in the interquartile range and the X marks the arithmetic mean The endpoints of the outward extending lines depict the minimum and the maximum values Components of a BOXPLOT Median Maximum Minimum 13at Quartile Mean 3rd Quartile br Oo ds 40 50 60 70 a0 30 Figure 7 4 The Components of a Boxplot The Examine option allows access to a screen that displays a ranked listing of data values and order statistics An example of this screen is displayed in Figure 7 5 The RecNo colunn indicates the samples sequence in the data file The lt up gt lt down gt lt pg up gt lt pg dn gt lt home gt and lt end gt keys may be used to scroll the display to the desired positon Pressing lt q gt will cause the Results screen and menu to appear EXAMINE DATA Data Value i Z Probit 9 WO Oo J Gy Un h Oo N ee 1 1 1 1 3 3 3 3 4 4 B B J Figure 7 5 Stat Examine Screen 7 6 THE HISTOGRAM OPTIONS MENU HISTOGRAM
22. Exponent plus kK The parameter Fraction specifies the number of characters in f If Fraction is less than or equal to zero f is omitted If Fraction is less than zero the decimal point is omitted If the label is exactly zero the single character 0 is used If the parameter type has the value Base k Each numeric label is written in the form GI fle The parameter exponent is ignored The value of e is k The parameter Fraction specifies the number of characters in f If Fraction is less than or equal to zero f is omitted If Fraction is negative the decimal is omitted Note that TU f expresses the value of Base Non exponent Labeling Setting label to No Exp selects non exponent notation The parameter exponent is ignored If the parameter Type has the value Base k Each numeric label is written in the form GI L E The parameter Fraction specifies the number of characters in f If Fraction is less than or equal to zero f is omitted If Fraction is less than zero the decimal point is omitted If the label is exactly zero the single character 0 is used If the parameter Type has the value _Base 10 k Each numeric label is written in the form GJ L E The parameter Fraction specifies the number of characters in T when k is zero If Fraction is less than or equal to zero f is omitted If Fraction is less than z
23. Files Execute Quit Files This option is used to specify two Geo EAS data file names The first is an input data file The second is an output file After the two files have been specified the variable names stored in the input file are displayed Execute This option appends a variable called Sequence to the current listing of variables displayed on the screen The variable name Sequence is appended to the variable names read from the input file These variable names are then stored in the specifed output file An example of such an output file is Out6 dat Out6 dat Demol dat ficticious data set 1 4 Easting feet Northing feet Arsenic ppm Sequence 320 0 311 0 850 l 119 0 119 0 630 2a 115 0 111 0 560 3 114 0 269 0 1 02 4 114 0 269 0 1 02 5 431 0 137 0 670 6 Merge Upon selection of this option the Merge menu is displayed The Merge menu provides the options necessary to merge two Geo EAS data files The details of this operation are discussed in the Execute option The menu line appears as follows Files Execute Quit Files This option is used to specify the names of two Geo EAS data files which are to te merged and the name of an output file which will contain the results The files to be merged cannot have the same file name or an error message appears Execute When this option is selected the Merge process is initiated After this process R complete the variables from the output file are displa
24. GE Grater than Greater than or equal to EQ NE Equal to Not equal to Upon selection of the Subsetting Condition optionthe variable names stored in the input file are displayed You are prompted for a variable for the Operand1 from a toggle field After the selection you are prompted for a logical operator from the toggle field After this selection control is passed to the Row Extract Operand menu The Row Extract Operand menu is the next menu discussed After a selection is made for the second operand control is returned to the Row Extract menu The Row Extract Operand menu provides the options necessary to select a variable or entera constant for Operand2 The menu line appears as follows Constant Variable Constant This option is used to specify a constant floating point number for Operand2 The constant is entered into a numeric field Ifa constant causes a numeric overflow then a message appears informing you of the error pressing any key returns control to the Row Extract Operand menu After a valid constant has been entered pressing lt enter gt returns control to the Row Extract menu Variable This option is used to specify a variable for the Operand2 The variable is selected from a toggle field After the selection pressing lt enter gt returns control to the Row Extrad menu Execute When selecting the Execute option the Row Extraction process is initiated Each sample of Operand1 described above is che
25. Line Type Color Use this option to create Lead 1 Black the graph The graph will Blue be saved in the file Red specified Yellow Green Brown Data Variables Symbol Line Regression Legend Graph Options Quit Generate the graph Figure 14 2 Xygraph Options Screen Data The Data option is used to enter the name of a Geo EAS data file Variables The Variables option allows the selection of variables that are to be used as the X and Y coordinate values The choices available are the variable names as specified in the data file The screen fields accessed from this option are X Variable A toggle field used for selecting the variable name whose values will be used as the independent variable on the graph The default X Variable is the first variable in the data file Y Variables Six toggle fields used for selecting the variables whose values will be used as the dependent variables in the graph The default Y Variable is the second variable in the data file Symbol Line The Symbol Line option allows the specification symbols and or lines and colorto mark the data on the graph The symbols and line types are displayed in Figure 14 3 The screen fields access from this option are Figure 14 3 Xygraph Symbols and Line Types Figure 14 3 Xygraph Symbols and Line Types No symbol No symbol Symbol Type Six toggle fields for selecting the type of symbol to plot There are six choices available 0 to 6 A value of 0 indica
26. Minimum Maximum N m 4 E 0 E S Ay a E Y ist Point in pair Figure 10 9 Vario Lag Scattergram Examine The Examine provides access to the Examine Lag Results screen displayed in Figure 10 10 The Examine Results screen displays in a tabular form a pair index number the first and second values the distance the direction and the difference squared for each pair in the lag These are sorted in order of difference squared You can use the arrow keys or the lt 1 gt to lt 9 gt keys scroll to a position on the screen Press lt End gt to position the list at the largest squared difference and lt home gt to view the smallest Type lt q gt to clear the screen and return to the Lag Results menu EXAMINE RESULTS ist Value 2nd Value Distance Direction Difference2 400 14 500 420 234 382 102 010 000 300 388 z84 178 102 010 400 000 954 223 152 108 160 600 200 005 72 746 108 160 Z0Q 600 936 74 521 207 50 246 83 300 Figure 10 10 Vario Examine Lag Results Screen Write The Write option allows you to save the lag results in a Geo EAS data file The Variable From__ To Distance Direction Difference and Difference 2 will saved in a file The file name is entered on the message line when the Write option is selected The default file name is LagResult dat If the file already exists a Yes No prompt provides an alternative to quit proceed The lag results file may be used with ot
27. Neighbors Point 366 666 180 000 320 286 246 266 Horthing 166 1268 86 246 326 466 480 366 Figure 12 5 Krige Debug Search Area Display 12 7 THE DEBUG DISPLAYS The debug displays are provided as a means of viewing intermediate kriging results during the kriging process Since such displays slow the kriging process the displays may be activated or de activated at any time during kriging If the lt num lock gt lt caps lock gt or lt scroll lock gt keys are activated during kriging the corresponding displays will be generated on the screen To continue to the next display the lt q gt keyis pressed To disable the generation of these displays the corresponding keys should be de activated On an IBM AT style keyboard these three keys are accompanied by status lights which indicate that the key is on or off The following is an explanation of each display and the key which activates it Debug results for variable Cadmium Point kriged is 360 000 300 000 a2CT ACI J 10 294 18 000 6 561 9 326 7 540 7 135 3 923 7 383 1 000 8 677 6 561 18 000 8 220 3 709 3 513 1 918 4 755 1 000 9 954 9 328 6 220 18 000 5 312 5 489 2 619 5 347 1 000 5 866 7 540 3 709 5 312 18 000 9 635 6 977 7 409 1 000 5 482 7 135 3 513 5 489 9 635 18 000 6 611 5 508 1 000 3 038 3 923 1 918 2 819 6 977 6 611 18 000 4 297 1 000 6 713 7 383 4 755 5 547 7 409 5 508 4 297 18 000 1 000 1 000 1 000 1 000 1 000 1
28. OPTIONS MENU The Graph Options screen and menu Figure 10 13 has options to select the graph titles and labels the spacing of the tick marks and the graph limits for the graph produced with the Plot option of the Variogram Modeling menu The menu line appears as follows Titles Tic Spacing Limits Qui GRAPH OPTIONS Titles Main Title Variogram for Cadmium Subtitle X Label Distance Y Label Variogram Tickmark Spacing Limits X Tickmark Spacing KX Axis Minimum 000 Y Tickmark Spacing X Axis Maximum 160 000 Y Axis Minimum 000 Y Axis Maximum Z 000 Titles Tic Spacing Limits Quit Flot the graph and model curve Figure 10 13 Variogram Graph Options Screen Titles The Titles option allows you to enter the title and labels for the graph The screen fields accessed from this option are Title An alphanumeric field which may contain up to 60 characters each for the title on the graph The default title contains the type of estimator and the variable name Subtitle An alphanumeric field which may contain up to 60 characters for the graph subtitle X Label An alphanumeric field which may contain up to 60 characters for the X axis label The default label is Distance Y Label An alphanumeric field which may contain up to 60 characters for the Y axis label The default label is the type of estimator selected Tic Spacing The Tic Spacing option allows the specification of the spacing of tickmarks o
29. The Variables Models screen and menu Figure 12 4 is provided for selection of the variables to krige and to specify the variogram model for each of the selected variables The Variables Models screen is divided into three areas The area on the left of the screen is used to display the list of variables selected for kriging called the Kriging List This list is used asa menu from which to select a variable when deleting or editing a variable model specification On the right the top area is for selecting new variables to add to the Kriging List and the bottom area is for entering variogram model parameters The Variables Models menu provides options to add or delete a variable and model to the Kriging List and to edit a set of variogram model parameters The menu line appears as follows New Variable Edit Delete Quit New Variable The New Variable option is used to select a variable to add to the Kriging List A toggle field is displayed in the top portion of the screen which contains the vanable names from the input file The default value for this field is the third variable name in the file Once this selection is made the variable name is added to the Kriging List and the variogram model parameters described below must be entered Note it is possible to krige the same variable more than once the output file will then contain duplicate variable names Edit The Edit option allows you to edit the specified variogram model for the
30. Xvalid Main Screen The Main screen and menu for Xvalid shown in Figure 11 1 provides options to specify the file prefix the input data file and variables and to access the Options Execute menu The menu line appears as follows Prefix Data Variables Options Execute Quit Prefix The Prefix option is used to enter the prefix for the data file name Data The Data option is used to specify the name of the Geo EAS data file to be used f cross validation This file must contain at least three variables consisting of two coordinates and a sampled value Variables The Variables option is used to select the coordinate and sample value variables They ar selected from toggle fields which contain the variable names from the specified data file The data file is accessed when these variables are selected If an error occurs while reading the data file an error message will be generated The screen fields accessed from this option are X Coordinate A toggle field for selecting the variable whose values represent the X coordinates for sample points The default X Coordinate is the first variable in the data file Y Coordinate A toggle field for selecting the variable whose values will be used as the Y coordinates for sample points The default Y Coordinate is the second variable in the file Variable to Krige A toggle field for selecting the variable to be estimated The default is the third variable in the data file Log Option A two value
31. and stores the data in the temporary file Each time a operation is performed the required data are retrieved from the temporary file and the newly generated data are stored in the temporary file A list of variable namesis displayed on the screen to indicate which variables reside in the scratch file If a variable is deleted using the Delete option from the Main menu then that data are deleted from the temporary file The variabe name is also deleted from the screen The Save option from the Main menu is used to move the data from the temporary file to the specified Geo EAS output data file 6 2 DATA LIMITS Trans reads as well as generates Geo EAS data files containing a maximum of 48 variables and 10 000 samples If a file should contain more than 10 000 samples then only the first 10 000 samples are read and a warning message is displayed If an attempt is made to create a 49th variable then an error messageis displayed 6 3 THE MENU HIERARCHY Trans __ Prefix Read Title Create _ New Variable________ Unary Operation Old Variable Binary Operation Indicator Transform Quit Quit Delete Save Quit Unary Operation _ Operation _____ Constant ___ _ Execute Variable Quit Quit Quit Binary Operation_____ Constant Operation____ Constant____ _ Execute Variable Variable Quit Quit Quit Quit Indicator Transform __ __Variable _ Cutoff Execute Quit 6 4 THE MAIN MENU TRANSFORMS 1 2 1 Data File Prefix NGe
32. assigned to samples minimizes the estimation variance which is computed as a function of the variogram model and locations of the samples relative to each other and to the point or block being estimated The standard error of estimation computed for a kriged estimate By definition kriging is the weighted linear estimate with the particular set of weights which minimizes the computed estimation variance standard error squared The relationship of the kriging standard deviation to the actual error of estimation is very dependent on the variogram model used and the validity of the underlying assumptions therefore kriging standard deviations should be interpreted with caution A distance class interval used for variogram computation A function frequently used when fitting mathematical models to experimental variograms often in combination with a nugget model A plot of mean absolute difference of paired sample measurements as a function of distance and direction Madograms are not true variograms and generally should not be used in kriging If used the kriged estimates might be reasonable but the kriging standard deviations will be meaningless v Glossary Nested Variogram Model Nugget Model Octant Search Ordinary Kriging Point Kriging Quadrant Search Range Relative Variogram Search Neighborhood Semi variogram Sill Simple Kriging Spherical Model Variogram Geo EAS 1 2 1 A model which is t
33. at a map of the data produced by the program Postplot Assuming that you have already copied the software and data into a directory called Geoeas on your hard disk and have used the command CD Geoeas to access the directory you can run Postplot either by 1 using the DOS command C GEOEAS gt Geoeas lt enter gt to enter the system menu moving the cursor to the Postplot option with the arrow keys and pressing lt Enter gt or by 2 running the program directly from DOS by typing the command C GEOEAS gt Postplot lt enter gt When the program begins execution it first displays a screen with introductory information When you press a key to proceed you will see the program main screen and menu as displayed in Figure 4 1 The bottom line on the screen provides the list of available options The first five move you to an area on the screen or to a new screen where you can input or select program parameters The Execute option starts the actual processing portion of the program and Quit moves you to the preceding menu or out of the program All menus in the system operate in a similar way options are selected by moving the highlighted bar to the desired option name with the arrow keys and pressing lt enter gt or by typing the first character of the option name POSTPLOT 1 2 1 A program for plotting 2D sample locations and values File Prefix C iNGeoEASNData Variables X coordinate variable Easting Y coordinate var
34. correctly you must disable the loading of such memory resident programs and re start the computer Programs in which this is likely to happen are Vario Statl Xygraph and Postplot Geo ES 1 z 1 Geostatistical Environmental Assessment Software Prevar Conrec Trans Vario Xygraph Postplot Stati Xvualid HPp lot Scatter krige View Use arrow keys to move cursor lt enter gt to select program Data preparation utilities FIG2 1 Geo EAS System Menu 2 2 2 Using the Programs From DOS To run the programs from DOS type the program name at the DOS prompt For example to start program Statl type STAT1 lt enter gt 2 3 ANSWERS TO COMMON QUESTIONS ABOUT GEO EAS gt Oo gt O amp O PF How do you pronounce Geo EAS Gee oh ease Then how come it s not spelled Geo EASE Next question I can t run all of the Geo EAS programs from the main menu What should I do DOS 4 0 and higher version do not leave enough room in memory for sane of the larger Geo EAS programs to run along with the menu The only solution is to run them directly from DOS This problem may also occur with any version of DOS when memory resident programs are present If executing from DOS doesn t work you may have to remove the memory resident programs How can I print Geo EAS graphics on my Laser Printer We are now including a public domain utility on the Geo EAS distribution diskettes which provides screen dump capability for HP Laserjet
35. from the file The data file is also accessed at this time so that the coordinate variable values may be loaded by the program If an erroroccurs while trying to access or read the parameter or data file a message will be displayed indicating the problem and any key may be pressed to return to the Main menu If parameters and data ate successfully loaded a message will be displayed and pressing any key will cause the Krige Options screen and menu to be displayed Options Execute The Options Execute option provides access to the Krige Options screen and menu See the section below for more information Save Parameters The Save Parameters options provides a means of storing program parameter values ina parameter file for later use When this option is selected a prompt is issued for the Output Parameter File name A default name is constructed with a kpf file extension as described above for the Read Parameters option If the named file already resides ondisk a Yes No prompt provides a means of overwriting the old file or exiting the option If an error occurs while trying to create or write to the Output Parameter File a message will be displayed and pressing any key causes re activation of the Main menu If the parameters are successfully stored in the file a message is displayed and a keystroke re activates the Main menu 12 5 THE OPTIONS MENU KRIGE OPTIONS Title Example grd kriged estimates of data from Example dat Data Grid
36. grd Contours for KSOCadmilum 240 Horthing NOEN s SED 420 480 EDD Easting Figure 4 24 Contours for Cadmium Kriging Standard Deviations This map illustrates the reasonable result that the highest kriging errars are predicted in areas with the lowest density of sample data 4 5 SUMMARY AND EXERCISES The example exercise just completed contained the basic elements of any geostatistical study You started with a sample data set conducted an exploratory statistical analysis interpreted the spatial correlation structure of the data and inferred an underlying variogram model and used the model to interpolate a grid of kriged estimates In the process you had to make a number of judgment calls which affected the results You treated the data set as representing a singe population You chose not to delete any outliers You chose to represent the spatial correlation structure of the data with an anisotropic exponential model plus a nugget term You accepted the default kriging option of ordinary block kriging with blocks approximated by a 2x2 grid T points Finally a conclusion was drawn that the default maximum of 8 samples in the kriging program should be increased Readers with little or no previous experience in geostatistical analysis may not feel comfortable with this entire process It is not always obvious which of these factors are most significant and which if any can be ignored Nor is it easy to define the
37. grid file Compare grd to plot contour maps of Cd1 Cd2 and Cd1 Cd2 Step 5 Run Scatter with the grid file Compare grd to plot Cd1 vs Cd2 Step 6 Run Statl with the grid file Compare grd to plot histograms of Cdl Cd2 and Cd1 Cd2 EXERCISE 2 Compare Point vs Block kriging Step 1 Run Krige with the data file Compare grd to create a grid file of kriged estimates called Comp1 grd Use the isotropic exponential model and krige Cd1 with ordinary point kriging Step 2 Repeat Step 1 with a grid file called Comp2 grd Krige Cd2 with ordinary block kriging 2x2 keeping all other parameters the same Step 3 Run Dataprep to merge Comp2 grd into Comp1 grd Step 4 Repeat Steps 3 6 from Exercise 1 using Comp1 grd These exercises can be repeated to make other interesting comparisons For example compare the results of kriging with a variogram model consisting of only a nugget term vs a spherical or exponential model with zero nugget Or compare kriging with a maximum of 4 samples vs 20 samples all other parameters being equal SECTION 5 DATAPREP 5 1 WHAT DATAPREP DOES Dataprep provides utilities for Geo EAS data files Dataprep has two divisions the DOS Utilities and the File Operations The DOS Utilities allows access to commonly used DOS commands The File Operations include utilities to manipulate Geo EAS data files The Dataprep File Operations use temporary files called Scratch Files for storing data read fro
38. liable for any damages losses or claims consequent to use of this software or documentation ABSTRACT This report describes how to install and use the Geo EAS Geostatistical Environmental Assessment Software software package on an IBM PC compatible computer system A detailed example is provided showing how to use the software to conduct a geostatistical analysis of a data set Thirteen Geo EAS programs are documented The principal functions of the package are the production of 2 dimensional grids and contour maps of interpolated kriged estimates from sample data Other functions include data preparation data maps univariate statistics scatter plots linear regression and variogram computation and model fitting Extensive use of screen graphics such as maps histograms scatter plots and variograms help the user search for patterns correlations and problems in a data set Data maps contour maps and scatter plots can be plotted on an HP compatible pen plotter Individual programs can be run independently the statistics and graphics routines may prove useful even when a full geostatistical study is not appropriate For ease of use the programs are controlled interactively through screen menus and use simple ASCII data files Geo EAS 1 2 1 ii Notice Disclaimer Table of Contents Sheets ec hs oe nee ec te ee 3 TABLE OF CONTENTS 0 0 0 0 0 0 cc eee eee eee ee ee eee 4 5 E 6 7 L 8 ACKNOWLEDGEMENTS anneuenn SECTION 1 I
39. names of the data file and an output grid file and we must select a variable and enter a variogram model The program computes a default 10x10 grid which we will usually want to override with more convenient ound numbers The default search ellipse is a circle with a radius about one fourth the maximum x or y dimension of the site which should be adequate for most cases The purpose of the search is to reduce computation time by eliminating from the kriging system of equations those samples which are unlikely to get significant weights The default search strategy is to treat the search circle as a single sector to examine all samples within it and use at least one but not more than the closest eight The number of samples required for kriging is related to the value of the nugget term in the variogram compared to the maximum variogram value possible within the search area The higher the nugget the more likely that more distant samples will get significant weights A rough rule of thumb would be to use eight samples when the nugget is near zero increasing to twenty when the nugget is more than 50 of the maximum value The more complex sector search options may be useful when you have unusual patterns or clusters of data We will accept the defaut search for now and check during kriging to see how well it works Initiate program Krige and the main screen will be displayed Figure 4 20 The Krige main menu allows you to retrieve previously s
40. not be plotted across a grid cell which contains a missing value After the graph see Figure 15 3 has been displayed type lt q gt to clear the screen and return to the Options menu Krging eettmatan produced Prom dota the Exarmpla grd Danteu r for Cadmium A30 240 Northing Figure 15 3 Example Contour Plot 15 6 THE GRAPH OPTIONS MENU GRAPH OPTIONS Axes Parameters Tick Parameters Major Ticmark Divisions Minor Divisions lt Major 2 Tickmark Label Format F10 0 F10 0 Ticmark Label Size ee 3 Titles Labels Main Center Subtitles Center Graph Limits 13 11 260 000 120 000 500 000 320 000 z0 000 z0 000 Main Title Kriging estimates produced from data file Example grd Subtitles Contours for Cadmium X Axis Easting Y Axis Morthing Tick Parameters Titles Labels Annotation Quit select the style for X and Y axes Figure 15 4 Conrec Graph Options Screen The Graph Options screen and menu Figure 15 4 provides control over the graph background Options are available to select the axis style the format for tickmark labeling and spacing and the character size and orientation of the graph titles and axis labels The menu line appears as follows Axis Parameters Tick Parameters Titles Labels Annotation Quit Axis Parameters The Axis Parameters option allows selection of the type of axis style for the X and Y axes The screen field accessed from this option is Axi
41. of 14 alpha numericcharacters Any valid DOS file name may be used The File Prefix discussed above is used to construct the entire file name when the file is accessed by the program If any errors occur while the programs are accessing or reading a data file a message indicating the problem will be issued Ifa file not found message is displayed the problem may be with the file prefix see above If no errors occur the variable names are read from the data file and stored into toggle fields for use by the Variables option Variable s This option is common to all programs which use Geo EAS data files It allows you to specify the variable or variables which the program will use Some programs only use one variable e g Stat1 and others require three e g CONREC Typically this option will provide access to one or more toggle fields which contain the variable names Some programs include additional fields for selection of other parameters related to the choice of variables These will be explained in the particular section which describes the program Execute This option is common to all Geo EAS programs It is used to initiate processng of data by the program Although the processing and interaction subsequent to the selection of this option is different for each program it shares the common function of initiation of processing The individual differences n processing will be described in more detail in the subsections which describe
42. of the sampled observations The estimated values associated kriging errors residuals and other useful statistics are displayed on a summary screen Scatter plots and histograms may be obtained for a quick summary of these results Results may be stored in a Geo EAS data file for further analysis 11 2 DATA LIMITS Xvalid requires that the input data file contains at least 3 but no more than 48 variables Two of these variables must represent the coordinates of sample locations No more than 1000 samples may reside in the data file If more than this number are encountered only the first 1000 values will be used for cross validation 11 3 THE MENU HIERARCHY Xvalid_____ Prefix Data Variables Options Execute ___ Type Quit Search Model Execute ____ Error Map Debug Scatter Plot Quit Histogram Write Examine Quit 11 4 THE MAIN MENU KUALIOD 1 2 1 A program for cross validating kriging parameters File Prefix C GeoEASSNDatas File Variables 5 Data points 60 Data File Name Exanple dat Missing data 0 Z Obs lt 0 Variables Opt ions Execute X coordinate East ing Use this option to specify the Y coordinate Northing XVALID kriging options screen This screen will be presented only Variable to krige Cadmium if a file and variables have been Log option DFF chosen Once options have been selected kriging may begin Prefix Data Variables St Ege Get Quit XVALID options screen Figure 11 1
43. on the same 360 kilobyte diskette with HERSHY BAR This means that if you only have 360 kilobyte disk drives and no fixed disk you will not be able to use these programs A separate working diskette may be prepared for each program subject to the restrictions mentioned above 2 2 INITIATING THE SYSTEM 2 2 1 Using the Geo EAS System Menu A program has been provided on the distribution diskettes which allows access to al programs from a common menu called the System Menu This file is named GEOEAS EXE Use of the system menu program requires that all program and suppott files reside on the same disk and subdirectory e g C GEOEAS To start the system menu program type GEOEAS lt enter gt A screen will be presented with the program names as in Figure 2 1 A highlighted bax cursor bar will appear on the screen The cursor bar may be moved around the screen by using the lt left gt lt right gt lt up gt or lt down gt keys When the cursor bar is positioned over a program name a short description of the program will appear at the bottom of the screen To initiate the described program press lt enter gt KKK Note KKK The Geo EAS system must have use of all available memory No memory resident programs such as SideKick may be loaded or the system menu program will not be able to load some programs If an error message occurs when using the system menu try to initiate the desired program from DOS If the program will not load
44. pcf Minimum 000 Min Distance 6 00 Maximum 16 7 Max Distance 302 Direction Direction Tolerance Max Bandwidth Lag Spacing 1 Z 3 4 5 6 7 8 9 Minimum Maximum Increnent New Lags Change Lags Post Plot Execute Quit Specify pair orientation selection criteria Figure 10 2 Vario Options Screen The Options screen and menu Figure 10 2 provides a means to specify variogram options view a post plot of the data and compute the variogram results The menu line appears as follows Direction New Lags Change Lags Post Plot Execute Quit Direction The Direction option allows you to specify the pair orientation selection criteria Figure 10 3 illustrates how these parameters affect the grouping of pairs within a lag interval The scren fields accessed from this option are Direction A numeric field for entering the pair direction in trigonometric degrees Acceptable values range from 0 to 180 degrees excluding 180 The default is zero degrees whicha direction parallel to the X axis Tolerance A numeric field for entering the direction tolerance in trigonometric degrees Acceptable value range from zero to 90 degrees inclusive The default is 90 degrees The tolerance is plus or minus For example a variogram computed with a direction of 90 degrees and a tolerance of 10 degrees will include all pairs with an orientation between 80 and 100 degrees Max Bandwidth A numeric field for entering the max
45. specified variable When this option is selected the Kriging List menu is activated A cursor may be moved to the appropriate member of the list with the lt up gt or lt down gt keys and selected for editing with lt enter gt Once the variable has been specified the parameters will be loaded onto the screen and the Variogram Model Parameters area will be activated In this screen area fields are provided for a nugget effect value and up to 4 additive variogram structures Each structure is specified with a structure type a sill value and an ellipse of influence If simple kriging is chosen a additional field is provided for entering the Global Mean Each of the four structures has five associated screen fields Selecting the Model option will cause a cursor bar to appear in the upper left corner of the models area The arrow keys may be used to move the cursor bar to fields in the Model area To exit the Model area move the cursor bar out of the top or off to the left of the area using the lt left gt or lt up gt keys If any errors are made when entering variogram model parameters an error message will be displayed and the cursor bar will be placed at the problem field The screen fields accessed from this option are Nugget A numeric field for entering the nugget value for the variogram model Only values greater than or equal to zero may be entered The defaut value is zero Global Mean A numeric field for specifying the global mean for sim
46. the debug displays on or off It is important to disable all three Debug Options prior to using the Execute option or intermediate results screens will be generated and kriging will proceed more slowly Block kriging Cadmium Cadmium lt 5 300 lt 7 606 lt 16 866 106 800 Missing H x Y ae vk N 143 SHH 328 8 87 2 20 3 Figure 12 3 Kriging Display If your personal computer is equipped with the proper graphics hardware a graphics display shown in Figure 12 3 is generated when the Execute option is selected In this display the original sample locations are represented by the x symbol As each point is kriged the estimates and associated results are displayed at the bottom of the screen except in Hercules equipped systems and the point or block estimates are plotted with a symbol which indicates the quartile of the estimate On EGA equipped computer systems these symbols and the sampk values are also color coded A legend is displayed at the right of the screen showing the symbols and corresponding quartile cutoff values If your computer system has no graphics capability no graph is displayed and the results are displayed at the bottom of the Krige Options screen During the kriging process the debug displays described below maybe activated or de activated to view intermediate kriging results Once all grid cells have been kriged a tone signals that the kriging has been completed Pressing lt q gt will cau
47. the file prefix should form the name of a valid metacode file or an error is displayed This file contains the metacode instructions produced by the programs Conrec Xygraph and Postplot VIEW 1 2 1 A metacode translator for EGA CGA or Hercules graphics configuration File Prefix C GeoEASNData Metacode Filename Metacode met Scale Square Adaptor EGA 640 x 350 Execute Use this option to display the plot Prefix File Scale Quit Display the plot Figure 16 1 View Main Screen Scale The Scale option is used to select the type of plotting area to use when displaying the graph The screen field accessed from this option is a toggle field The choices available are Square the original scaling of the graph and Rectangle the graph will be stretched to fit the entue screen The default is Rectangle Execute The Execute option is used to display the graph on the screen When this option is selected the metacode file is read and translated into graphic output for the type of graphic system in use If a problem is encountered while trying to read the metacode file an error message will be displayed This can occur if the specified file is not in the correct format The metacode file can contain more than one graph frame To View subsequent frames press lt enter gt After the graph has been displayed type lt q gt to clear the screen to return to the Main menu SECTION 17 HPPLOT 17 1 WHAT HPPLOT D
48. the software so that you may repeat the exercise as a tutorial or to test the software The scenario for the example is that data has been acquired from analyses of 60 soil samples at a site contaminated with arsenic cadmium and lead The basic objectives are to examine tle data set for possible errors or outliers and to construct contour maps of each of the variables to define the areas of highest concentration In this example you will work primarily with the variable Cadmium you are encouraged to try out these procedures with the arsenic or lead data The Example Data Set The Example dat data set is an ASCII file in the Geo EAS format It contains data from 60 sample locations The file structure is described in Section 3 above The first few lines are as follows Example dat Geostatistical Environmental Assessment Software 5 Easting feet Northing feet Arsenic ppm Cadmium ppm Lead ppm 288 0 311 0 850 11 5 18 25 285 6 288 0 630 8 50 30 25 273 6 269 0 1 02 7 00 20 00 280 8 249 0 1 02 10 7 19 25 4 2 EXPLORATORY DATA ANALYSIS The first order of business in any data analysis is to become familiar with the data set You will use a combination of statistics and graphical displays to look at the range and shape of the frequency distribution to look for data outliers which may be erroneous or unrepresentative to look at the spatial coverage of the data and to look for spatial patterns in the data Begin by taking a look
49. the value of the exponent in the numeric labels along the X and Y axes Graph Limits The Graph Limits option allows you to enter values that specify the coordinate limits and the type of scaling for the X and Y axes Certain combinations of the Tick Parameters will cause these values to be overridden The screen fields accessed from this option are Min Max Scale Two numeric fields for entering the minimum coordinate value to be used on the X and Y axes The default values displayed are determined from the data file for the variable selected as the X and Y variables Two numeric fields for entering the maximum coordinate value to be used on the X and Y axes The default values displayed are determined from the data file for the variable selected as the X and Y variables Two toggle fields for selecting the type of scaling to be used on the X and Y axes The choices available are Linear and Log natural log scaling If Log scaling is selected and any data values are negative or zero an error message is displayed and the Scale field is reset to Linear The default is Linear Titles Labels The Titles Labels option allows you to enter the title and labels for the graph The Hershy character sets of 33 fonts are used for plotting alphanumeric labels Also certain special characters may be embedded in the title or label which control selection of alternate fonts or other aspects of the plotted text These special chara
50. values Interpretation of results however can often be difficult Unusually large differences between estimated and true values may indicate the presence of spatial outliers or points which do not seem to belong with their surroundings In kriging the process of approximating the area of a block by a finite array of points A function frequently used when fitting mathematical models to experimental variograms often in combination with a nugget model A function frequently used when fitting mathematical models to experimental variograms often in combination with a nugget model A methodology for the analysis of spatially correlated data The characteristic feature is the use of variograms or related techniques to quantify and model the spatial correlation structure Also includes the various techniques such as kriging which utilize spatial correlation models A variogram computed by subtracting lag covariances from the sample variance This approach compensates for cases where in directional variograms the mean of the say west members of the sample pairs is not the same as the mean of the east members InvCov is a rather obscure term referring to the fact that some probabilistic assumptions underlying the variogram computation are no longer necessary Inverted Covariance variograms may be modeled and used in kriging in the same way as ordinary variograms A weighted moving average interpolation method where the set of weights
51. 000 1 000 1 000 1 000 000 Figure 12 6 Krige Debug System of Equations Display lt caps lock gt This activates the Search Area display shown in Figure 12 5 For each estimate the search ellipse is displayed along with all sample locations inthe sampled area The neighbors which were chosen for the estimate are marked The coordinates of the estimated point center of the search ellipse is displayed at the top of the screen If more than one sector was chosen the sector boundaries will be plotted This display may be used to check if the search ellipse is of the proper size and orientation and that the desired number of samples are used as neighbors On a non graphics system this display is a text display showing the list of neighbors the sample locations and the sector number for each neighbor Debug results for variable Cadmium Point kriged is L 360 000 180 000 Ci YLL Uci Distance Uci Bei 370 180 6 10 9 60 384 11 2 360 195 6 80 15 0 142 8 68 370 165 6 70 17 8 165 8 58 350 203 8 30 24 9 324E 01 6 79 334 194 11 6 29 9 123 8 22 334 163 8 70 31 4 124 7 62 346 210 10 8 33 3 128E 01 5 46 360 216 10 1 36 0 171E 91 4 63 Neighbors D Weights 1 000 Estimate 7 50 CUU 11 389 ok 1 62 WiBb2i 9 290 ak 2 61 D 510 Figure 12 7 Krige Debug Kriging Weights Display lt scroll lock gt This key activates a display Figure 12 6 which shows the system of equations used to produce the estimate A one dim
52. 2 Variables that exist in both input files i e have identical variable names will be combined into ore variable with the records of Filel preceding those of File2 The difference is that for Filel variables the records normally occupied by File2 variables are filled with missing values 1 E 31 For File2 variables the records normally occupied by Filel variables are filled with missing values As an example the output file Outl dat was generated when Demo1 dat above as File1 and Demo 2 dat above as File2 were appended Out1 dat is shown below Out1 dat Demol dat ficticious data set 1 4 Easting feet Northing feet Arsenic ppm Lead ppm 320 0 311 0 850 10E 32 119 0 119 0 630 10E 32 115 0 111 0 560 10E 32 114 0 269 0 1 02 10E 32 114 0 269 0 1 02 10E 32 431 0 137 0 670 10E 32 102 0 164 0 10E 32 300 122 0 137 0 10E 32 360 116 0 119 0 10E 32 700 150 0 315 0 10E 32 500 148 0 291 0 10E 32 710 Column Extract Upon selection of this option the Column Extract menu is displayed The Column Extract menu provides the options necessary to create a Geo EAS data file with variables extracted from an input file The menu line appears as follows Files Variables Execute Quit Files This option is used to specify two file names The first an input file is a Geo EAS data file The second file is a Geo EAS output file Variables This option is used to specify one or more variables which will be extracted and written
53. 3x3 and Block 4x4 which is used to indicate point or block krigng If one of the Block NxN choices is selected block estimates will be produced The N refers to the number of discretizatim points used to approximate the area of the block Large N values give somewhat better approximations of the blocks at the expense of increased computing time The choice of point or block also determines the meaning of the Grid Origin parameters If block kriging is chosen these parameters refer to the center of the lower left hand block in the grid Grid The Grid option is used to specify the variables to use as coordinate values the origin of the grid the size of grid cells and the number of cells inthe X and Y directions These are specified with four screen fields for each of the two directions The screen fields for the X and Y directions are Variable Origin Cell Size Cells Search Two toggle fields containing the variables names from the specified input data file which are used to specify the variables to be used as the sample coordinate values when kriging The default values for the X and Y variables are the first and second variables in the data file Once the variables have been chosen the coordinate values are retrieved from the data file If an error occurs during the retrieval of data a message is displayed and pressing any key will re activate the Krige Options menu but it is assumed that the file is corrupted and cann
54. 8 6 712 700 10 217 6 483 500 08Z 418 400 828 572 100 765 335 200 332 868 500 658 842 600 390 610 600 83 63 000 402 598 249 291 438 162 200 600 Cw ww B MA ooo UH LQ 4 LP LG WON ON M L LU 2 LQ L LQ L M LU Figure 11 9 Xvalid Examine Results Screen SECTION 12 KRIGE 12 1 WHAT KRIGE DOES Krige is an interactive program which performs two dimensional kriging A rectangular grid of kriged estimates is created and stored in a Geo EAS data file Contour plots may be generated from these gridded estimates with the program Conrec Options are provided to control the type of kriging the neighborhood search area the grid spacing and extents and the variogram model for each variable kriged Up to ten variables may be kriged in each program execution Tle program parameters may be stored in a parameter file and retrieved for later use During the kriging process debug displays may be activated or de activated for the purpose of viewing intermediate kriging results 12 2 DATA LIMITS Krige requires that the input data file contains at least three but no more than 48 variables Two of these variables must represent the coordinates of sample locations Up to ten variables may be selected for kriging No more than 1000 samples may reside in the daa file If more than this number are encountered only the first 1000 values will be used for kriging 12 3 THE MENU HIERARCHY Krige __ Prefix Read Param
55. 8 Statl Histogram SECTION 8 SCATTER 8 1 WHAT SCATTER DOES Scatter produces scatter plots of variable pairs ina Geo EAS data file Options allow for log and semi log plots and for a regression line to be calculated Scaling and numeric tickmark labeling for the axes and titles are computed automatically 8 2 DATA LIMITS Scatter requires that the input data file contain at least three but not more than 48 variables These should consist of an X and Y coordinate and a third variable which wil be posted The data file may contain up to 10000 samples If the data file contains more than 10000 samples only 10000 will be used by Scatter 8 3 THE MENU HIERARCHY Scatter___ Prefix Data Variables Options Execute Quit 8 4 THE MAIN MENU The Main menu and screen Figure 8 1 has the options to allow specification of the data fik name the selection of the variables to be used and other program opttons The menu line appears as follows Prefix Data Variables Options Execute Quit Prefix The Prefix option is used to enter the prefix for file names SCATTER 1 2 1 A program for producing scatter plots File Prefix C GeoEASSData Data File Example dat Data records 60 Missing data 0 Variables X Variable Cadmium Log Off Execute Y Variable Lead Log Off Use this option to create the plot Options Regression Yes Equal Scaling No Prefix Data Variables Options Quit Generate the plot Figure
56. DEL PLOT lt Q gt Variogram for Cadmium Parameters File Examp le pct Pairs 1342 Direct AAA Tol AAA MaxBand na E L H fe D H L gt Cadmium Limits Minimum Max imum Mean Var 80 Distance Figure 4 14 Variogram with Exponential Model Lag Spacing 10 Now repeat the above option sequence with a lag increment of 25 The resulting graph i displayed in Figure 4 15 Variogram for Cadmium Parameters File Examp le pct Pairs 1462 Direct HHA Tol AAA MaxBand na Cadmium Limits E L N an D H L gt Minimum Maximum Mean Var 80 126 Distance Figure 4 15 Variogram with Exponential Model Lag Spacing 25 As you can see the ability to define the true variogram structure is limited by the particular set of data available The best you can do is to find a model which fits reasonably well over a range of lag spacings Both of the two models proposed earlier are satisfactory In practice kriging estimates calculated with the two variogram models will be almost identical Kriging standard deviations however are more sensitive than the estimates to changes in the variogram model as well as to differences between the real world and the assumptions underlying the kriging equations For this reason it is generally not wise to interpret kriging standard deviations as a true measure of the estimation error For the remaining discussion of va
57. Direction New Lags Change Lags Post Plot Execute _Type Plot BoxPlot Lag Results ___ Histogram Scatter Plot Examine Write Quit Model __ C Model Plot Options___ _ sTitles Tic Spacing Limits Quit Quit Quit Quit Quit 10 4 THE MAIN MENU WARIO 1 2 1 A program for computing var iograms File Pref ix C GeoEASNData File 3 Kept R Obs lt 8 Pair Comparison File Example pcf Missing 68 Z 4 Variable Variable Cadmium Variogram Options Log Option Off Use this option to display the Variogram Options Screen and menu Limits Variogram options may be selected Minimum and the variogram may be computed Maximum Prefix Data Variable Limits Miika Quit Specify variogram options compute Figure 10 1 Vario Main Screen The Main screen and menu shown in Figure 10 1 has options to allow specification of the pair comparison file the selection of the variable to be used with associated options and the variable limits The menu line appears as follows Prefix Data Variable Limits Options Execute Quit Prefix The Prefix option is used to enter the prefix for file names Data The Data option is used to enter the pair comparison file name The pair comparison file contains distances directions and pair pointers for pairs of 2D sample points in a Geo EAS data file This file is produced by the program Prevar and is a binary non readable file to conserve disk space Variable The Vari
58. ECTION7 STATI 7 1 WHAT STAT1 DOES Sat is an interactive program which computes basic univariate statstics and displays histograms or probability plots for variables in a Geo EAS data set Options are available for calculating statistics on the natural log of the selected variable for specifying a variable to be used asa weighting factor and for performing calculations on subsets of the input data through the use of upper and lower limits A Batch Statistics option has been included which will produce a report of statistics for all variables in the specified data file 7 2 DATA LIMITS Statl requires that the maximum number of variables in the input data file not exceed 48 The data file may contain up to 10 000 samples If the data file contains more than 10 000 samples then only 10 000 will be used by Stat 7 3 THE MENU HIERARCHY Stat Prefix Data Variable Limits Execute ___ Histogram ___ _ Type Class Limits Axes Titles Results View Graph Quit Probability Examine Quit Batch Statistics Quit 7 4 THE MAIN MENU STAT 1 1 2 1 A program to compute univariate descriptive statistics File Prefix geoeas File Variables 5 Data records 64 Data File Name example dat Missing Data H 2 Obs lt 8 Variable Variable Cadmium Execute Weight None Log Option Off Use this option to compute and display the statistics A menu Limits of additional graphs and options will be displayed
59. ENDIX A REFERENCES x x 00000000 177 APPENDIX B NCAR GRAPH OPTIONS 0 0 0 0 eee eee eee 178 APPENDIX C HERSHY CHARACTER FONT TABLES 181 APPENDIX D POLYGON FILE FORMAT 184 Geo EAS 1 2 1 iv March 1991 GLOSSARY OF GELOS TA TIS TIC AL TERMS Anisotropy Block Kriging Covariance Cross Validation Discretization Exponential Model Gaussian Model Geostatistics Inverted Covariance InvCov Variogram Kriging Kriging Standard Deviation Lag Linear Model Madogram Geo EAS 1 2 1 In geostatistics the situation where a variogram exhibits a longer range i e better correlation in one direction than another Estimating the value of a block from a set of nearby sample values using kriging In Geo EAS the block area is approximated by a 2x2 3x3 or 4x4 array of points centered on each specified grid node A Statistical measure of the correlation between two variables In geostatistics covariance is usually treated as the simple inverse of the variogram computed as the overall sample variance minus the variogram value These covariance values rather than variogram values are actually used in the Geo EAS kriging matrix equations for greater computational efficiency A technique for testing the validity of a variogram model by kriging each sampled location with all of the other samples in the search neighborhood and comparing the estimates with the true sample
60. Geo EAS There is disagreement in the geostatistical literature as to which term should be used Geo EAS uses variogram for simplicity The upper limit of any variogram model which has such a limit i e which tends to level off at large distances In Geo EAS the spherical gaussian exponential and nugget models have sills For the linear model sill range is used merely to define the slope A variety of kriging which assumes that local means are relatively constant and equal to the population mean which is well known The population mean is used as a factor in each local estimate along with the samples in the local neighborhood This is not usually the most appropriate method for environmental situations A function frequently used when fitting mathematical models to experimental variograms often in combination with a nugget model A plot of the variance one half the mean squared difference of paired sample measurements as a function of the distance and optionally of the direction between samples Typically all possible sample pairs are examined and grouped into classes lags of approximately equal distance and direction Variograms provide a means of quantifying the commonly observed relationship that samples close together will tend to have more similar values than samples far apart vi March 1991 ABBREVIATIONS Throughout this manual keyboard keys are expressed in lower case and enclosed in angle bracket
61. If the Log option is on then LN precedes the variable name Y Axis An alphanumeric field which may contain up to 60 characters for the Y axis The default label is Frequency Results The Results option allows access to the Histogram Results screen and menu Figure 7 7 This screen displays the histogram results The results are in tabular form The display may be scrolled as in the Examine option described above View Graph The View Graph option allows access to a screen that displays the histogram Figure 7 8 The resulting histogram is accompanied by a box plot described in the Probability Plot Option of the Results menu and some univariate statistics HISTOGRAM RESULTS Data File C NGeoEASNData Exanple dat Variable Cadmium Lower Limit 600 Class Min Upper Limit 16 700 Class Width lt Upper Limit Freq Sum Weights Rel F Max Value Class Mean D LD GD s G Ln LQ MA K Un ee COLT eon OF fe OO OF rA LH L j ze T or L keys to Scroll or lt Q gt to Quit Figure 7 7 Statl Histogram Results Screen Histogram Data file Example dat Statistics N Total 64 N Miss 4 N Used 64 Mean 885 Variance 531 Std Dev 94i z C Y 981 Skeuness 151 Kurtosis 464 a N E u 2 a y N IV Minimum HHH 25th x 368 Median 956 foth x 806 E Maximum 766 B 12 Cadmium ppm Figure 7
62. NTRODUCTION 1 1 OVERVIEW ar LRR be shea Line Beek Sek T RATE Bogie OG A Ged PO Gee Be moe 10 1 2 EQUIPMENT REQUIREMENTS 0 0 10 1 3 GEO EAS AVAILABILITY 0 0 00 0c eee nae re 1 4 USER PROFILE 3 2 25 termene mti rmen EREE ES epee Spee So pth Hgok A Moka Pyar ee wees SECTION 2 SYSTEM SUMMARY 2 1 INSTALLING THE SYSTEM ennenen 12 2 1 1 The Distribution Diskettes runerne eneee 12 2 1 2 Hard Disk Installation 0 0 0 0 eee eee eee 13 2 1 3 Using the Programs on Floppy Diskette annene 13 2 2 INITIATING THE SYSTEM 00 0 eens 13 2 2 1 Using the Geo EAS System Menu ennannann arun run rnn 13 2 2 2 Using the Programs From DOS 00000000 e ee eee es ANSWERS TO COMMON QUESTIONS ABOUT GEO EAS 3 1 DATA Fosen Nene doe eee teehee Sheil tee Bee Pee Goal Bee ose 17 3 1 1 Geo EAS Data Files 17 3 1 2 File Naming Conventions 0 0 0 0 eee eee eee 19 3 1 3 System Defaults Option 0 0 eee ee 19 3 2 INTERACTIVE SCREENS x x K eee 19 32 1 Screen Format 0 ook Send oh eee Bee eae eee eee Lea oE 19 3 2 2 Types of Screen Input Fields 000 0 0000 21 3 2 3 The Menu Tree eeue Seeded a eee hea ope R eet h eg ees es 22 3 2 4 Common Menu Options 00 0 eee 23 3 3 GEO EAS GRAPHICS K Rg K 0 0 RRR RRR RRR RN nea a En TA E E K 24 3 3 1 On Screen Graphics 0 0 0 eee 24 3 3 2 Metacode Based Graphics 0 0 0 0 25 3
63. Number of Sectors and the Max Points per Sector parameters indicate the maximum number of samples to be used for kriging This parameter also serves to indicate the number of groups to use for classification of neighbors The search ellipse is divided into the chosen number of equally sized sectors If a sample is found to be within the search ellipse it is flagged with a sector number These sector numbers and sample distances are used for elimination of samples which exceed the Max Points per Sector criterion a toggle field for selecting the maximum number of points which a sector may contain The choices range from 1 to a maximum which depends on the number of sectors chosen If one sector is specified up to 24 neighboring points may be used If four or eight sectors are selected the choices are constrained such that a maximum of 64 neighbors may be retained If the number of neighbors in a sector exceeds the specified value the farthest samples as determined by Distance Type are eliminated from consideration a toggle field for selecting the minimum number of neighboring samples to use for kriging The default value or this parameter is 1 If fewer than the specified number are found kriging is not performed and a missing value is generated for the estimate and kriging standard deviation a toggle field for selecting the maximum allowable number of consecutive sectors with no neighbors The choices available are determined by
64. OES Hpplot translates the device independent plotting instructions in metacode files into a file of HPGL plotting commands The output file can be routed to a HP plotter by setting up the serial port COM1 by running the batch file HPSETUP BAT and then using the DOS PRINT command to send the file to the plotter The HP plotters supported are HP 7470 2 pen plotter HP 7475 6 pen plotter HP 7450 8 pen plotter If the HP 7470 is used for plotting the graph will be plotted in two pen colors the program does not prompt for pen changes 17 2 THE MENU HIERARCHY Hpplot Prefix T File Scale Execute Quit 17 3 THE MAIN MENU The Main screen and menu Figure 17 1 has the options to allow specification of the metacode and output file names and the plotting area The menu line appears as follows Prefix File Scale Execute Quit Prefix The Prefix option is used to enter the prefix for file names HPPLOT_ 1 2 1 Translates a metacode file into HPGL plotting instructions File Prefix C GeoEASNData Input Filename Metacode met Output Filename etacode plt Scale Square Enter the Enter the output file ane O O file name Prefix File Scale Execute Quit Figure 17 1 Hpplot Main Screen File The File option is used to enter the metacode file name The screen field accessed from ths option is an alphanumeric field and may contain up to 14 characters This character string combined with the file prefix should form the na
65. Operand One menu provides the options to select operand for the binary operation The menu line appears as follows Constant Variable Quit Constant This option is used to assign aconstant value to the binary operand one This option is similar to the constant option noted in the Unary Operand menu section described earlier The exceptions are that the wording in the messages refers to the binary operand one and not the unary operand and upon entering a valid constant value control is passed to the Binary Operation menu described below If the constant value is unacceptable then control is returned to the Binary Operand one menu Variable This option is used to assign an existing variable to the binary operand one Ths option is similar to the variable option noted in the Unary Operand menu section described earlier The exceptions are that the wording refers to binary operand one and not the unary operand and upon making the selection control is passed to the Binary Operation mem described below The Binary Operation menu provides the option to select a binary operator The menu lire appears as follows Operations Quit Operation This option is used to specify the binary operator You are prompted for a binary operator from a toggle field Upon making the selection control is passed to the Binary Operand Two menu described below The Binary Operand Two menu provides the options to select operand for the binary operation
66. Operation menu provides an option to select a unary operation The menu lire appears as follows Operations Quit Operation This option is used to specify the unary operator You are prompted for a unary operator from the toggle field Upon making the selection control is passed to the Unary operand menu described below The Unary Operand menu provides the option to select an operand for the unary operation The menu line appears as follows Constant Variable Quit Constant This option is used to assign a constant value to the unary operand You are are prompted for the constant value The constant value is entered into a numeric floating point field The default value is initially zero If the value entered results in a numeric overflow then a message is displayed Upon pressing any key control is returned to the Unary Operand menu If the constant value entered is acceptable then control is passed to the Execute menu described below Variable This option is used to select an existing variable for use as the unary operand from a toggle field Upon making the selection control is passed to the Execute menu described below The Execute menu provides the option necessary to initiate any unary operation The menu line appears as follows Execute Quit Execute This option is used to initiate the unary operation During processing the message Processing data is displayed on the screen After processing is complete the mini
67. Parameters Data File Example dat x Y Output File Example grd Variable Easting Northing Origin 260 000 120 000 Polygon Spacing 20 000 20 000 Number 13 11 Polygon File Sample Select No search Parameters Type Ma jor Radius 59 400 Sectors Minor Radius 59 400 Max in Sector Type of Kriging Ordinary Ellipse Angle 000 Min to use Point or Block Block 2x2 Distance Type Euclidean Empty Sectors Data Polygon Type Grid Search Miscia Title Execute Quit This option invokes the Variables and Variogram Models screen Figure 12 2 Krige Options Screen The Options screen and menu Figure 12 2 has the options to specify the parameters to be used for kriging and to initiate the kriging process The menu line appears as follows Data Polygon Type Grid Search Variables Models Title Execute Quit Data The Data option is used to specify the name of the Geo EAS data file whose values will be used for kriging and the name of the Geo EAS output file of gridded estimates The screen field accessed through the Data option are Data File A 14 character alphanumeric field in which the name of the input data file is entered The most recently used Geo EAS data file name is the default Once the name is given the program reads the variable names from the file into several toggle fields used for selecting the coordinate variables and the variables to krige If the data file cannot be located or an error occurs while accessing t
68. S COM information about HPPS COM HPPS COM screen dump capability for HP Laserjet HPPS DOC document file for HPPS COM HPPS ASM source file for HPPS COM HPPSREAD ME information about HPPS COM 2 1 2 Hard Disk Installation To install the system on a fixed disk a subdirectory should first be created for example GEOEAS For information about creating subdirectories refer to the DOS reference manual All files on the distribution diskettes should be copied into the subdirectory For more information on how to copy files from a diskette into a subdirectory refer to your DOS user s manual Approximately three megabytes 3 million bytes of storage R required If insufficient disk space is available for all files to reside together on fixed disk programs must be initiated from DOS and the system menu GEOEAS EXE may not be used 2 1 3 Using the Programs on Floppy Diskette The fact that all programs and support files cannot reside on one floppy diskette has several implications Since the system menu program requires that all files be present on the same disk and subdirectory the system menu may not be used to run the programs they must be initiated from DOS Since several programs require the presence of HERSHY BAR p operate correctly it is important that both the executable file and HERSHY BAR reside on the same diskette Unfortunately the size of the executable files for programs XYGRAPH POSTPLOT and CONREC are too large to fit
69. The menu line appears as follows Constant Variable Quit Constant This option is used to specify a constant for the binary operand two This option is similar to the binary operand one constant option described previously in the Binary Operand One menu The exceptions are that the wording refers to operand two and not operand one and upon entering an acceptable value control is passed to the Execute menu described below Variable This option is used to specify an existing variable for binary operand two It is similar to the binary operand one variable option described previously in the Binary Operand One menu The exceptions are that the wording refers to operand two and notoperand one and upon making a selection control is passed to the Execute menu described below The Execute menu provides the option needed to initiate the binary operation The menu line appears as follows Execute Quit Execute This option initiates the binary operation During processing the message Processing data is displayed on the screen The Execute binary option causes the same prompts as in the Execute option of the unary operation Refer to the Execute option of the Execute mem discussed previously in the Unary operation section As noted previously the operatia exponentiation may result in a numeric overflow causing the program to abnormally terminate crash Indicator Transform The indicator transform is an operation requiring two operand
70. United States Environmental Monitoring EPA 600 8 9 1 008 Environmental Protection Systems Laboratory April 1991 Agency Las Vegas NV 89193 3478 Research and Development SEPA GEO EAS 1 2 1 User s Guide pee p ppp EPA 600 4 88 033 MARCH 1991 GEO EAS 1 2 1 GEOSTATISTICAL ENVIRONMENTAL ASSESSMENT SOFTWARE USER S GUIDE by Evan Englund U S Environmental Protection Agency Environmental Monitoring Systems Laboratory Las Vegas Nevada 89193 3478 Allen Sparks Computer Sciences Corporation 4220 S Maryland Parkway La Plaza B Suite 408 Las Vegas Nevada 89119 ENVIRONMENTAL MONITORING SYSTEMS LABORATORY OFFICE OF RESEARCH AND DEVELOPMENT U S ENVIRONMENTAL PROTECTION AGENCY LAS VEGAS NEVADA 89119 NOTICE The information in this document has been funded wholly or in part by the United States Environmental Protection Agency under Contract 68 01 7325 to Computer Sciences Corporation 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 DISCLAIMER Geo EAS software and documentation are provided as is without guarantee or warranty of any kind expressed or implied The Environmental Monitoring Systems Laboratory U S Environmental Protection Agency Las Vegas NV and Computer Sciences Corporation will not be
71. Y PROCEDURES Known bugs Xyegraph or Postplot may fail when certain incompatible combinations of axis tickmark parameters are chosen This is dependent upon the data configuration and choice of parameters and is due to internal limitations in the NCAR graphics utilities which these program use Postplot may produce undesirable scaling in plots with certain sample data configurations An attempt is made by the software to produce true proportion post plots The underlying NCAR utilities which produce the metacode files sometimes override the scaling specified by Postplot This is a unexplainable phenomenon which has not and unfortunately will not be corrected Trans may crash when an operation is chosen which would produce a very large or very small number An example would be the operation 1 0 X or 10 X when X is very small or very large 1 E 1000 1 E1000 This type of program error cannot be trapped or handled by Trans In such cases the result cannot be produced due to hardware limitations in the precision of the numeric coprocessor or floating point emulation software Since there is no remedy for this situation The only solution is to avon such operations Avoiding User Induced Errors There are several error conditions which the program was specifically not designed to check for These involve checking to see if disk or printer peripherals are connected and ready for data transfer You are reponsible for ensuring that printers a
72. a sets The data limit remains at 1000 records The screen fields accessed from this option are Fraction A numeric field for specifying the cutoff value Acceptable values range from 0 to 1 If the value entered is less than 1 a uniform random number between 0 and 1 is generated for each pair and the pair is retained only if the random number is less than the value entered The default is 1 Seed A numeric field used for entiring the seed to initialize the random number generator The default random seed is computed from the system clock If a Geo EAS data file has 600 observations for example the number of possible pairs R 179 700 Specifying a fraction of 0 089 will result in a random subset of approximately 16 000 of these pairs in the Pcf file which may be analyzed with VARIO If the subset option is used several subsets should be evaluated to ensure that they are giving consistent results The use must choose whether to use the limit or the subset option or both Execute The Execute option is used to initiate computation of pair comparison data and the creation of the pair comparison file Distances and pair directions for all pairs in the data file are computed subject to the limits criteria sorted by distance and saved in the pair comparison file If the limit of 16384 pairs is reached a Yes No prompt will allow an opportunity to quit or proceed If this occurs and you choose to proceed 16384 pairs will be written to the fi
73. able option allows for the selection of the variable that is to be used to compute the variogram The choices available are the variable names as stored in the pair comparison file When the variables are selected the input data are read from the data file and defaults are computed for sample value limits and lag spacing If and error occurs while reading the file an error message is displayed The screen fields accessed from this option are Variable A toggle field for selecting the variable whose values are used as the sample values The default Variable is the third variable in the pair comparison file Log Option A two valued toggle field to enable or disable a logarithmic transformation of the samples The choices available are On use logarithmic scaling and Off The default is Off Limits The Limits option allows you to enter the values that specify the limits for the sample values The screen fields accessed from this option are Minimum A numeric field for entering the minimum variable value to use in computation The default value is the minimum value of the variable selected Maximum A numeric field for entering the maximum variable value touse in computation The default value is the maximum value of the variable selected Options Execute The Options Execute option provides access to the Options screen and menu Figure 10 2 described below 10 5 THE OPTIONS MENU OPTIONS Variable Cadmium Pair File Example
74. ages full screen data entry parameter files and graphical displays are used to provide a high degree of interactivity and an intimate view of results Users may easily alter parameters and re calculate results or reproduce graphs providing a what if analysis capability Geostatistical methods are useful for site assessment and monitoring situations where data are collected on a spatial network of sampling locations and are particularly suited to cases where contour maps of pollutant concentration or other variables are desired Examples of environmental applications include lead and cadmium concentrations in soils surrounding smelter sites outdoor atmospheric NO concentrations in metropolitan areas and regional sulfate deposition in rainfall Kriging is a weighted moving average method used to interpolate values from a sample data set onto a grid of points for contouring The kriging weights are computed from a variogram which measures the degree of correlation among sample values in the area as a function of the distance and direction between samples Kriging has a number of advantages over most other interpolation methods Smoothing Kriging smoothes or regresses estimates based on the proportion of total sample variance accounted for by random noise The noisier the data set the less individual samples represent their immediate vicinity and the more they are smoothed Declustering The kriging weight assigned to a sample is l
75. aller size may be better suitable for output to a plotter This field is ignored if the Annotation option No Annotation is chosen The Spline option allows the specification of the amount of smoothing of the line segments The screen field accessed from this option is a numeric field Acceptable values range from 2 5 to 30 The larger the Spline Tension value the less smoothing of the line A value of 30 disables smoothing Smooth contours generally look better but because the contour lines are smoothed independently smoothing results in contour lines which may intersect The default value is 15 0 SECTION 16 VIEW 16 1 WHAT VIEW DOES View displays on the screen the graphs contained in metacode files The graphs can be displayed on a EGA CGA or Hercules graphics system Color graphs are viewed on EGA systems On CGA and Hercules systems monochrome graphs are displayed 16 2 THE MENU HIERARCHY View______ Prefix File Scale Execute Quit 16 3 THE MAIN MENU The Main screen and menu shown in Figure 16 1 has the options to allow specification of the metacode file name and the plotting area The menu line appears as follows Prefix File Scale Execute Quit Prefix The Prefix option is used to enter the prefix for file names File The File option is used to enter the metacode file name The screen field accessed from this option is an alphanumeric field and may contain up to 14 characters This character string combined with
76. alues can be computed for all options providing instant results Options allow control of contour levels labeling and smoothing Options to control axes labeling and titles are also available A file called a metacode file is created for redisplay or producing a hardcopy 15 2 DATA LIMITS Conrec requires that the input data file contains at least three but not more than 48 variables These should consist of at minimum an X and Y coordinate and a third variable for which contour lines will be drawn The data file may contain up to 10000 samples These must form a grid with no more than 100 elements in each direction If these limits are exceeded the grid cannot be formed and the data file cannot be used by Conrec 15 3 THE MENU HIERARCHY Conrec Prefix Read Parameters Option Execute__ Data Variables Graph Options _____ Axes Parameters Tick Parameters Titles Labels Annotation Quit Contour Options____ New Levels Edit Levels Labeling Dash Pattern Annotation Save Parameters Execute Spline Quit Quit Quit 15 4 THE MAIN MENU CONREC 1 2 1 A contouring program for gridded data File Prefix C GeoEASSData Input Parameter File Data File Name Output Parameter File X Variable Y Variable Contour Variable Pref ix Use this option to enter a pref ix Graph Limits x Y which is used to build file names used by the program Pts Minimum Max imum Size Read Parameters Options Execute Save Paramete
77. ample report with the sequence option enabled follows Example output from the Report option Page 1 Demol dat ficticious data set 1 Easting Northing Lead Arsenic bs feet feet ppm ppm 1 320 0000 311 0000 8500000 1 000000 2 119 0000 119 0000 6300000 2 000000 3 115 0000 111 0000 5600000 3 000000 O Sort Upon selection of this option the Sort menu is displayed The Sort menu provides the options necessary to sort a variable in ascending order If a selected variabk s sample has to be relocated then the entire record associated with that sample is also moved An example of the Sot operation is shown in the Execute option The menu line appears as follows Files Variable Execute Quit Files This option is used to specify two Geo EAS file names the first is the input file and the second is an output file Variable This option is used to specify the variable to be sorted You are prompted fora variable which is selected from a toggle field After the selection pressing any key returns control to the Sort menu Execute Upon selection of this option the specified variable is sorted in ascending order When the process is complete the data are stored in the specified output file A message appears informing you that the data have been sent to the output file Upon pressing any key control is returned to the Sort menu As an example the following output file Out4 dat was generated when the variable Easting of the input f
78. and direction away Experimental variograms plot the average difference actually one half the squared difference or variance of pairs of measurements against the distances separating the pairs If you had measurements at all possible sample locations you could compute the true variogram for a site i e the variance of all pairs of measurements which satisfy each combination of distance and direction In practice with limited data you compute the variances for groups of pairs of measurements in class intervals of similar distance and direction You then plot a graph of the variances versus distance for a particular direction and fit a model curve to the graph the model is assumed to be an approximation of the true variogram Continuing with the example we will use Prevar to create an intermediate file of data pairs and Vario to compute plot and model variograms No automatic model fitting is provided we will use Vario to superimpose plots of various model curves on the experimental variogram until we find one that looks right Prevar is a simple program with only a few options to allow you to reduce the number of sample pairs in the output file to the maximum allowed by Vario by setting minimum and maximun limits on X and Y and by setting a maximum distance for pairs This is necessary when the number of samples in the data set exceeds 181 Upon initiating Prevar the main screen will be displayed as in Figure 4 7 PREVAR
79. appears as follows Unary Operation Binary Operation Indicator Transform Quit Unary Operation This option provides access to the Unary Operation menu The Unary Operatim menu described below is the first of three menus that provides options needed to complete a unary operation After a selection is made from one menu control is passed to the succeeding menu The Unary Operation menu provides a selection of unary operators Next the Unary Operand mem provides the choice of a constant or an existing variable for the operand Finally the Execue menu provides the Execute option The unary operations perform an operation on one operand The operations are shown below as they would appear in the toggle field sqrt Computes the square root of an operand log Computes the base 10 logarithm of an operand In Computes the natural logarithm of an operand truncate Truncates the operand exp Computes e to the power of x exp where e is 2 71828 and x is the operand Note that a numeric overflow can result in using the exp operation In such a case the program will abnormally terminate crash rank Determines the rank of an existing variable This operation assigns an integer value to the result variable based upon the rank of a specified existing variable in a sorted list equals Set the variable equal to the operand abs val Computes the absolute value of the operand sign Changes the sign of the operand The Unary
80. ariable is deleted from the temporary file and from the list of variable names on the screen Subsequent to entering your choice control is returned to the Main menu Save When the Save option is selected the data stored in the temporary file are written to a specified data file A prompt is issued for the output Geo EAS data file name If blanks are entered then an error message is displayed If the output file already exists then a Yes No prompt will appear asking if the file should be overwritten The data in the temporary file is copied to the output Geo EAS data file If an error should occur while opening the output file then an error message is displayed While the file is being saved the message Writing data appears After the data has successfully been written a message is displayed press any key to continue 6 5 THE CREATE MENU The Create menu provides the options necessary to perform transformations to a Geo EAS data file The menu line appears as follows New Variable Old Variable Quit New Variable When the New Variable option is selected a new variable is created in the scratch file The new variable takes on values generated from the specified operation unary binary indicata transform You are prompted for the new variable name If the given variable name is blank then a message to this effect appears pressing any key returns control to the Create menu If the variable name already exists then a warning message appe
81. ars pressingany key passes control to the Operation menu If the variable name is unique to the scratch file then you are prompted for a description of the measurements The field for the measurements description can accept up to 10 alphanumeric characters After entering the measurements description control is passed to the Operation menu described below Old Variable This option is used to specify an existing variable whose contents are replaced by the results of the specified operation unary binary indicator transform You are prompted for a variabk from the toggle field After making the selection you are asked if you wish to change the variable s current name or measurements description When indicating yes you may retain or change the name by entering up to 10 alphanumeric characters into the field If blanks ate entered then an error message is displayed you are then returned to the alphanumeric field and prompted for another variable name If the given variable name is the same as the existing variable then a message appears and you are prompted for a new variable name You are then prompted for a measurements description The measurements description of the old variable is displayed by default You may retain or enter another description Pressing lt enter gt causes the Operation menu described below to be activated 6 6 THE OPERATION MENU The Operation menu provides a selection of transformation operations The menu line
82. aved kriging parameters or to save the parameters you have just used before exiting the program Because this is your first attempt with this data set you must use the Options Execute option to go directly to the Options screen and menu This screen is displayed in Figure 4 21 ERIGE 1 2 1 A program for kriging a grid of estimates File Prefix C GeoEASSNData Read Parameter File Input Paraneter File Pref ix Use this option to enter a prefix which is used to build file names save Parameter File used by the progran Output Parameter File Read Parameters Options Execute Save Parameters Quit Enter the Prefix for files Figure 4 20 Krige Main Screen K RIGE OPTIONS Title Example grd kriged estimates of data from Example dat Data Data File Example dat Output File Example grd Polygon Polygon File Sample Select No Type Type of Kriging Point or Block Ordinary Block 2x2 Grid Parameters Variable Origin Spacing Number x Y East ing Northing 260 000 1260 000 20 000 z0 000 13 11 Search Parameters Ma jor Radius Minor Radius Ellipse ngle Distance Type Euclidean Sectors 1 Max in Sector 16 Min to use H Enpty Sectors 0 pd Data Polygon Type Grid Search ar iables Mode ls Title Execute Quit This option invokes the Variables and Variogram Models screen Figure 4 21 Krige Options Screen Use the following option sequenc
83. ble line rectangle at the bottom of the screen frame This area is used to display program error messages yes no prompts prompts for additional information or instructions for using a program option C The Menu Line This is the line of text located just below the screen frame It contains a set of menu option names and a highlighted box cursor bar The cursor bar can be moved along the menu line by using the lt left gt and lt right gt cursor control keys As the cursor bar is moved over a menu option name a shot description of the menu option is displayed on the line just below the menu line This line is called the menu description line In addition on the main screen for each program more detailed descriptions of the menu options are displayed You may explore the possible choices in a program by moving tle cursor bar and reading the descriptive messages which accompany each menu option To select a menu option move the cursor bar over the desired menu option name and press lt enter gt An alternative and faster way to select menu options is to press the key which corresponds to the first letter in the menu option name The result is the same as using the cursor control keys and pressing lt enter gt In program Statl for example you would choose to enter the data file name by pressing lt d gt for the Data option from the main menu D Parameter Groups Typically a functionally related group of program input parameters fi
84. bottom and the maximum value at the top The rectangle superimposed over the vertical range line is the inter quartile range The bottom on this rectangle is the first quartile and the top is the third quartile Therefore 50 of the data falls within the range represented by the rectangle The mean is represented by x and the median is represented by the horizontal line through the rectangle The distance h is plotted along the horizontal axis and the difference squared is plotted on the vertical axis The variable name is displayed in the title of the graph Vertical and horizontal axes scaling and the tick mark spacing are calculated by the program Displayed on the right side of the graph is the number of pairs the lag minimum and maximum the direction tolerance and max bandwidth the variable minimum and maximum and the mean and variance of the data Boxplot for Cadmium Parameters File Example pct Pairs 1388 Direct HHA Tol 668 MaxBand Tea Cadmium Limits k 0 N L E a 0 0 N E Q 4 DI kal H Qa 6 Minimum Max imum Mean Uar Distance Figure 10 6 Vario Box Plot Lag Results When Lag Results option is selected you will be prompted to select a lag number before access is provided to the Lag Results screen and menu This is accomplished by using the lt up gt and lt down gt keys to move the cursor bar to the desired lag number and pressing lt enter gt
85. c 10 11 Complex Special Characters 12 Complex Roman 13 Complex Greek 14 Complex Italic 15 17 Complex Special Characters 18 19 Duplex Roman 20 21 Complex Script 22 23 Complex Cyrillic 24 25 Triplex Roman 26 27 Triplex Italic 28 Gothic German 29 Gothic English 30 Gothic Italian 31 Gothic Special Characters 32 Centered Symbols Certain special characters are used to inform the graphics software that this font information is to be used for plotting These characters may be embedded in graph titles or labels and will allow selection of alternate font types and other special features These special characters are not plotted but are instead interpreted as commands by the metacode translator software The special characters and their meanings are backspace one character position indicates a three digit font selection code follows selects the default font lt subscript the next character gt superscript the next character The figure below illustrates the results of using the following five characters strings 004Geostatistical Environmental Assessment Software 027Geostatistical Environmental Assessment Software 007Geostatistical Environmental Assessment Software _Geostatistical Environmental Assessment Software _ Special characters 003k 010Q 010t 008p Easting M gt 2 Figure C 1 Example font selection codes Font 004 Geostatistical Environmental 4ssessment Software Font 029 ro sata cal
86. ciated data file name Quit This option is common to all Geo EAS programs It is used to exit from a menu or program Using the analogy of the Menu Tree the quit option allows you to move up one level in the tree When the quit option is used from the main menu of a particular program a Yes No prompt is issued Do you really want to quit lt Y N gt The lt q gt key is typically used to select this option The Yes No prompt isa means of ensuring that a series of lt q gt keystrokes will not cause inadvertent termination of the program 3 3 Geo EAS GRAPHICS 3 3 1 On Screen Graphics Many Geo EAS programs have graphics capability Each such program uses graphics in one of two ways Programs Statl Vario Xvalid and Krige plot graphics directly on the screen This approach is used to provide a quick look at data or program results Such graphics displays may be printed ona dot matrix printer but may not otherwise be saved or modified When a graphics screen is displayed the program will wait for a key to be pressed Pressing lt q gt will cause an interactive screen and menu to be displayed Pressing lt p gt will produce a hard copy of the screen on a graphics printer It i important to make sure that a graphics printer is connected to your computer if you choose this option or the program will lock up Also make sure that the printer is turned on and online If the program locks up you will probably have to re start the com
87. cked to see if it satisfiesthe test condition If so then that entire line of data is extracted from the input data file and stored in a temporary file After this process is complete the data from the temporary file are stored in the output file When the data have been stored to the output file and the execution complete you are informed witha message stating that the data has been sent to the output file If no samples satisfy the tet condition then a message appears and no data are stored Inboth cases pressing any key returns control to the Row Extract menu As an example of the Row Extraction operation the following output data file Out2 dat R generated when Demol dat is the specified input file and the test condition is Easting LE Northing Out2 dat Demol dat ficticious data set 1 3 Easting feet Northing feet Arsenic ppm 119 0 119 0 630 114 0 269 0 1 02 114 0 269 0 1 02 Each data record in Demol1 dat is examined by the program If the est condition is true then that line in the file is extracted and stored in the specified output file Only those records satisfying the specified logical expression will be extracted and stored in the output file Compress Upon selection of this option the Compress menu is displayed The Compress menu provides the options necessary to compress a Geo EAS data file Thisoperation eliminates any duplicate data records that appear in a specified input Geo EAS data file and stores the resul
88. cters are not plotted but are interpreted as commands by the metacode translator software The file HERSHY BAR included with the software contains the font information See the appendices for more information on font selection codes The screen fields accessed from this menu option are Main title Subtitles X Label Y Label Reset An alphanumeric field which may contain up to 60 characters for the main title of the graph The default title contains the variable name selected as the post variable and the name of the data file Two alphanumeric fields which may contain up to 60 characters each for the subtitles on the graph The subtitles appear below the main title An alphanumeric field which may contain up to 60 characters for the X axis label The default label is composed of the X variable name followed by its units in parentheses An alphanumeric field which may contain up to 60 characters for the label on the Y axis The default label is composed of the Y variable name followed by its units in parentheses The Reset option allows the user to reset the parameters to their default values SECTION 15 CONREC 15 1 WHAT CONREC DOES Conrec produces contour maps of variables with gridded coordinates in a Geo EAS data file The data must form a complete grid A grid is a a set of values with equally spaced X and Y coordinates which form a rectangle Individual grid cells may contain missing values Default parameter v
89. d On Off toggle field for enabling or disabling the Log Option If the Log Option is set to On kriging will be performed on the natural log of the sample values If it is set to Off no log transformation will occur The default value for the Log Option is Off Options Execute The Options Execute option provides access to the Options screen and menu See the sectim below for more information 11 5 THE OPTIONS MENU OPTIONS Data File GeoEAS Data Example dat X Variable Easting search Ellipse Parameters Y Variable Northing Distance type Euclidean kriging Cadmium R Major 86 6448 Num sectors 1 Log option Off R Minor 86 HBH Max pts sector 8 fing le BBH Min pts to use 1 Kriging Type Ordinary Min Dist 468 Empty sectors B Variogram Model Nugget 5 664 Global Mean Type Sill Ma jor Range Minor Range Ellipse Angle Spherical 11 444 146 444 166 HHH 444 1 Z 3 4 Type Search Model Debug Quit Begin kriging the sample values Figure 11 2 Xvalid Options Screen The Options screen and menu shown in Figure 11 2 has the options to specify the parameters to be used for kriging and to initiate the cross validation process The menu line appears follows Type Search Model Execute Debug Quit Type The Type field is a toggle field used for selecting the type of kriging used in cross validation The choices are Ordinary and Simple If Ordinary is chosen ordinary point kriging
90. d used them to develop the Xygraph and Postplot programs Naser Heravi and Russell Peterson of CSC provide on going maintenance and upgrades David Gonzales of EMSL LV wrote routines for identifying PC hardware configurations and assisted with the metacode device drivers We gratefully acknowledge the advice and encouragement provided by Andre Journel throughout the development process We are also indebted to the many people who provided constructive reviews of the software and user s guide including Randal Barnes of the University of Minnesota Dave Grundy of the U S Geological Survey Stan Miller of the University of Idaho Brent Huntsman of Terran Corporation John Rogers of Westat and William P Smith and James C Baker of the USEPA Finally we would like to thank the many users of version 1 1 who sent in the bug reports comments and suggestions which made version 1 2 1 possible Evan J Englund Allen R Sparks Geo EAS 1 2 1 Vili Acknowledgements SECTION1 INTRODUCTION 1 1 1 2 1 3 OVERVIEW Geo EAS Geostatistical Environmental Assessment Software is a collection of interactive software tools for performing two dimensional geostatistical analyses of spatially distributed data Programs are provided for data file management data transformations univariate statistics variogram analysis cross validation kriging contour mapping post plots and line scatter graphs Features such as hierarchical menus informative mess
91. e aren t any simple answers The best model is the one which most closely matches the true variogram for the site but of course you will never know what that is unless you exhaustively sample the site Although some form of least squares criteria could be used in Geo EAS the selection must be made subjectively simply by picking the model that looks like the best fit Sometimes the error distributions obtained from cross validation can help you to decide which Fortunately the differences between the spherical and exponential models above will only cause minor differences in the kriged estimates so that either one would be an acceptable choice If you look at variograms computed at different lags it will become obvious that the experimental variograms contain quite a bit of noise The shape of the experimental variogram changes as the lag spacing changes and the model which appears to fit best at one lag spacing may appear to be the worst at another Try a lag spacing of ten units The graph of Figure 4 14 will be displayed Variogram for Cadmium Parameters File Examp le pct Pairs 1388 Direct 668 Tol HBA MaxBand nia E 4 an D H L gt Cadmium Limits Minimum Maximum Mean Var 80 Distance Figure 4 13 Variogram with Exponential model nugget 4 5 Sill 13 5 Range 160 OPTION ACTION FIELD VALUE QUIT QUIT NEW LAGS Accept Minimum 0 Accept Maximum 150 Input Increment 10 EXECUTE MO
92. e Search option above In fact the variogram ellipse of influence is defined exactly as the search ellipse with two ranges radii and an angle Note that the second ellipse is used to select a reasonabk subset of neighbors for efficient kriging it has no relationship to the variogram model ellipse s Minor Range a numeric field for indicating the length of the minor shorter range of the variogram ellipse This value must be less than or equal to the Major Range non zero and non negative The default value is the Major Range value If the two ranges are equal an isotropic variogram structure is defined If they are not equal the two ranges are used to determine the anisotropy ratio Ellipse Angle a numeric field for indicating the orientation of the ellipse for the variogram structure It is given in trigonometric degrees in the range from zero up to but not including 180 and indicates the angle between the longest axis of the ellipse specified by the Major Range and the sample coordinate X axis If the two ranges are equal isotropic structure then the angle is ignored Execute The Execute option is used to initiate kriging All parameters must be specified before kriging may begin Several Debug Options described below are enabled or disabled with the lt caps lock gt the lt num lock gt and the lt scroll lock gt keys These keys are used to toggle the debug displays on or off If your keyboard has status lights for th
93. e dat the default Pair Comparison File would be Example pcf If the file already exists a Yes No prompt provides alternatives to continue or quit from the option Variable The Variable option allows the selection of the variables that are to be used for the X and Y coordinate values The choices are determined by the variable names in the input data file The screen fields accessed from this option are X Variable A toggle field used for selecting the variable name whose values will be used as the X coordinates The default X variable is the first variable in the data file Y Variable A toggle field used for selecting the variable name whose values will be used as the Y coordinates The default Y variable is the second variable in the data file Limits The Limits option is used to restrict the area and interpair distance for pairs retained in the pair comparison file The screen field accessed from this option are Minimum Three numeric fields for entering the minimum X and Y coordinate values and the minimum distance between pairs The default values displayed are determined from the coordinate variables in the data file Maximum Three numeric fields for entering the maximum X and Y coordinate values and the maximum distance between pairs The default values displayed are determined from the coordinate variables in the data file Subset The subset option is used to permit sub sample variograms to be computed from large dat
94. e keys it is easy to determine the state of each key It is important to disable all three Debug Options prior to using the Execute option or intermediate results screens will be generated and kriging will proceed more slowly If your personal computer is equipped with the proper graphics hardware a graphics display is generated Figure 11 4 when the Execute option is selected In this display the original sample locations are represented by symbols The symbol coding is used to classify the input data into their respective quartiles As each point is kriged the estimates and associated results are displayed at the bottom of the screen and the original symbols are over plotted by symbols which represent the value of the estimate On EGA equipped computer systems the symbols are also color coded If your computer system has no graphics capability or has a Hercules graphics card no graph is displayed and the results are displayed at the bottom of the Options screen During the kriging process the debug displays described below may be activated de activated to view intermediate kriging results Once all sample values have been kriged a tone signals that the kriging has been completed Pressing lt q gt at this time will cause the Results screen and menu described below to be displayed 320 Cadmium 280 Z 5 300 lt 7 600 n 246 Oo Z 16 866 E gt 10 800 r 200 a Missing N S z 168 126 80 246 320 400 480 566 Easti
95. e to specify the file names and grid parameters and to proceed to the next menu Figure 4 22 OPTION ACTION OPTIONS EXECUTE DATA Accept Accept Accept Accept Input Input Input Input Input Input GRID FIELD Data File Grid File X variable Y variable X origin Y origin X cell size Y cell size X cells Y cells VALUE Example dat Example grd Easting Northing 260 120 20 20 13 11 VARIABLES MODELS Variables and Models Selection List of Variables Variable Cadmium Global Mean to Krige Cadmium 9 Variogram Model Parameters Nugget 4 500 Major Range Minor Range Angle 1 Z 3 4 5 6 l 300 000 7 8 J 0 1 Edit Delete Quit pd a new variable and model to the Kriging List Figure 4 22 Krige Variables Models Screen The following option sequence selects Cadmium as the variable to be kriged enters the variogram model executes the kriging routine and saves the parameter file OPTION ACTION FIELD VALUE NEW VARIABLE Toggle Variable Cadmium Input Nugget 4 5 Toggle Type Exponential Input Sill value 13 5 Input Major range 300 Input Minor range 100 Accept Angle U QUIT EXECUTE lt Q gt QUIT SAVE PARAM Accept Parameter file Example kpf Upon selection of the Execute option the program first displays a color coded sample location map on the screen and then overlays this with a color coded shaded grid cell as each kriged estimate is computed At the bottom of the
96. ebug screens reveala problem with the search or variogram parameters and you wish to change them and re start It is important to remember that the terminate kriging keys will not work when any of the three debug display keys is active 11 6 THE RESULTS MENU RESULTS Data File C GeoEAS Data Exanple dat X Variable Easting Y Variable Northing Krig ing Cadmium Data used Type Ordinary Missing data Variable Estimate Difference Kriging Std ZSCOrE Minimum 25th tile Median 75th tile Maximum N Mean Std Dev Scatter Plot Histogram Write Examine Quit Map of kriging error differences Figure 11 5 Xvalid Results Screen The Results menu and screen shown in Figure 11 5 is displayed when kriging has been completed The Results screen contains information about the data file variables and the type of kriging used Additionally descriptive statistics are provided for the original sample values the kriged estimates the kriging standard deviations the differences between estimate and observed and the zscore The zscore is computed as the ratio of the difference to the kriging standard deviation The Results menu appears at the bottom of the screen and provides options to display several graphs to examine the individual results and to save the results to a Geo EAS data file Graph scaling titles and labeling are performed automatically On a non graphic computer system the graphs are not generated
97. ed Missing values must be indicated by the code 1E31 Geo EAS won t read my data file What should I do Check to make sure that the number in line 2 is equal to the number of variable name lines and the number of variables per row Make sure that the data table contains no characters other than the exponential E If you used a worl processor or editor make sure that the file was saved as an ASCII or DOS Text file If the file was created or modified by Geo EAS programs it is possible that values were generated which are too large for the format specifications resulting in strings of instead of the corresponding values To prevent this expand the format specifications or you can remove them entirely the default isn t pretty but should always work A final quirk krige will not read a file from a floppy disk when the drive is specified in the Prefix field with a backslash e g a KRIGE failed when I ran it using a Gaussian variogram model What happened Unfortunately the Gaussian model doesn t always work particularily when you have a low nugget and or closely spaced data The only solution is to use one of the other models I have extra memory on my computer Can I expand the data limits in Geo EAS No Not yet anyway Future releases of Geo EAS will probably support more memory on DOS systems SECTION 3 SYSTEM OPERATION 3 1 DATA 3 1 1 Geo EAS Data Files All programs in the system use a common fo
98. een They will appear temporarily on the message line A Yes No prompt will typically have the form Question lt Y N gt To respond Yes press the lt Y gt key to respond in the negative press any other key A typical Yes No prompt is the Do you really want to Quit lt Y N gt prompt which is displayed after the Quit terminate program option is selected Some menu choices will result in prompts for additional information These promps for additional information will appear on the message line and may be of the alphanumeric numeric or toggle type 3 2 3 The Menu Tree The programs in the Geo EAS system require imput typically from data files and through interaction on the screen These program imputs are arranged in a hierarchy of functionally related groups Each group or individual program parameter value is accessed through a nenu of choices Some choices will lead to other nemus while some will lead to prompts for groups of one or more imputs Such an arrangement can be represented in a menu tree as illustrated below for program Stat1 Example menu tree Stat ___ Prefix Data Variable Limits Execute _______ Histogram ___ Type Class Limits Axes Title Results View Graph Quit Probability Plot Examine Quit Batch Statistics Quit In the Stat menu tree as in other programs some menu choices will lead to program inputs and some will produce numeric or graphical results This hierarchy of options and results
99. eir numeric values The choices available are Yes plot values No do not plot values The default value is No Two toggle fields for selecting the character size to use when plotting the values or symbols The choices available are 0 to 10 where 0 is the smallest and 10 is the largest character size The default size for plotting values is 5 and the default for plotting symbols is 4 These choices work well on the screen however a smaller size might be more suitable for output to a plotter A toggle field for selecting the scaling factor to apply to the values to be plotted The choices available range from 104 4 to 1044 The scaling factor shifts the decimal place left orright in the plotted value For example a scale factor of 10 4 applied to a value of 7 208 would result in the value 72080 being plotted If the Include Values field is set to No this choice is ignored If the default of 1040 is used the decimal place will not be shifted A toggle field for selecting the number of digits to display The choices available range from 0 to 3 For example selecting 2 with a value of 72 208 would result in the value 72 21 round up does occur being plotted The default is 1 one digit to the right of the decimal place A two valued Yes No toggle field to enable or disable the plotting of symbols at the sample locations The choices available are Yes plot symbols No do not plot symbols If the
100. elds are enclosed together on the screen by a single line rectangle These groups of parameters are accessed through the menu When a menu option is selected as described above a cursor bar appears at the screen field and a message describing what action to take appears on the message line When such a group contains several fields the cursor control keys or lt enter gt are used to move to subsequent fields Exiting from the last field in the group will return the cursor bar to the menu line In some programs parameter groups are arranged in a tabular fashion rows and columns To return to the menu line from such a group move the cursor bar to the left or bottom of the group with the lt left gt or lt down gt keys 3 2 2 Types of Screen Input Fields Several types of input fields are provided to allow flexibility in program parameter specification Below is a list of these types and an example of each field type in the Stat1 screen Alphanumeric Fields These fields may contain character strings of alphabetic or numeric characters Any alphanumeric characters may be entered The Prefix and Data menu options in Statl require alphanumeric values to be entered To specify adata file name select the Data option on the menu and type the name of the input data file Numeric Fields Only numeric data may be entered into numeric fields Some numeric fields will only accept integer non decimal numbers The programs will respond to an
101. elow is an example of a polygon file containing an inclusive square polygon with an exclusive triangular polygon in the center 2 Number of polygons 0 4 Inclusive 4 vertices 0 0 lst vertex 0 100 2nd vertex 100 100 3rd vertex 100 0 Last Vertex 1 3 Exclusive 3 vertices 25 25 lst vertex 75 25 2nd vertex 50 75 3rd vertex END OF FILE Note No blank lines may be embedded in the file
102. ensional array of values on the left of the screen shows the covariances between the estimate location and the neighbors and the matrix of values in the remaining portion of the screen shows the covariances between neighboring samples If the number of neighbors used in the system of equations is more than eight each row of the matrix will wrap around to the next line and produce an undesirable results This display allows you to see the actual covariance values used for kriging for comparison with other programs or for verification of results lt num lock gt This key activates the Kriging Weights display shown in Figure 12 7 Ths display provides information about the neighboring samples used for kriging each estimate This includes the coordinate values the sample values the distances from the estimated point and the kriging weights assigned to each neighbor Also displayed are the kriging estimate the kriging standard deviation and several related statistics including the sum of the kriging weights the kriging variance and the Lagrange parameter value SECTION 13 POSTPLOT 13 1 WHAT POSTPLOT DOES Postplot produces a plot of 2D sample locations and values for a variable in a Geo EAS data file Sample locations may be marked with a symbol value or both The format for the value to be plotted may be specified by setting a scaling factor and the number of decimal places to be used in the plotted value Options allow control of a
103. ept of the line represented by the equation Y Slope X Intercept The Slope Intercept and R Squared value a measure of correlation are displayed to the right of the graph The default value for Regression is Yes Equal Scaling A two valued Yes No toggle field to enable or disable the use of equa scaling on the plot If Equal Scaling is selected the true X and Y proportions are maintained on the screen If this option is not enabled the graph will be scaled to fill the screen The default value is No disabled Execute The Execute option is used to display the plot on the screen After the graph has been displayed type lt q gt to clear the screen and return to the Main menu Figure 8 2 displays an example scatter plot Scatter Plot from data file Example dat Regression Results Pairs Slope Intercept Correl coeff Cadmium Figure 8 2 Scatter Plot SECTION 9 PREVAR 9 1 WHAT PREVAR DOES Prevar is a preprocessor program for the program Vario All variogram calculations use the distance and relative direction between pairs of points in the sampled area Prevar computes these so that variogram parameters may be changed and variograms recalculated more quickly in Vario The output from Prevar is a pair comparison file PCF The pair comparison file contains the input data file contents along with distances and relative directions between pairs of sample points This information is used by the pr
104. ero the decimal point is omitted For example if Fraction 1 Base 3 6 and k ranges from 3 to 3 The labels produces are 0036 036 36 3 6 36 360 and 3600 If the parameter Type has the value _Base k Each numeric label is written in the form G L L If k is greater than or equal to zero and in the form 1 E E if K is less than zero The parameter Fraction specifies the number of characters in f when K is equal to 1 If Fraction is less than or equal to zero f is omitted If Fraction is less than zero the decimal point is omitted For example if Fraction 1 Base 2 And k ranges from 4 to 4 the labels produced are 1 16 1 8 1 4 1 2 4 8 16 APPENDIX C HERSHY CHARACTER FONT TABLES The Hershy character set consists of 33 different character fonts numbered 0 through 32 This information is stored in a machine readable file called HERSHY BAR which is included with the software distribution The font descriptions indicate the extent to which the characters contain tapered segments simplex duplex complex triplex or gothic and the size of the characters cartographic indexical or centered symbol The following table lists available fonts and font codes FONT DESCRIPTION 0 Cartographic Roman 1 Cartographic Greek 2 Simplex Roman 3 Simplex Greek 4 Simplex Script 5 6 Simplex Special Characters 7 Complex Roman 8 Complex Greek 9 Complex Itali
105. es of covariance rather than variance The Inv Cov variograms have the same units measurement units squared as ordinaty variograms and may be modeled and used for kriging in the same way Relative variograms are unitless decimal fraction squares When modeled and used for kriging the relative kriging standard deviations must be multiplied by the estimated values to be comparable with kriging standard deviations produced with ordinary variogram models 4 4 KRIGING AND CONTOURING The program Krige produces a regular grid of interpolated point or block estimates using either Ordinary or Simple kriging The default option ordinary block kriging is recommended for most environmental applications Point kriging usually provides estimates very similar to those from block kriging but if a point being estimated happens to coincide with a sampled location the estimate is set equal to the sample value This is not appropriate for contour mapping which implicitly requires a spatial estimator Ordinary kriging estimates the point or block values with a weighted average of the sample values within a local search neighborhood or ellipse centered on the point or block Simple kriging also assigns a weight to the population mean and is n effect making a strong assumption that the mean value is constant over the site it also requires that the available data be adequate to provide a good estimate of the mean In order to execute Krige we must provide the
106. eters Options Execute ___ Data Save Parameters Polygon Quit Type Grid Search Variables Models __ New Variable Title Edit Execute Delete Quit Quit 12 44 THE MAIN MENU ERIGE 1 2 1 A program for kriging a grid of estimates File Prefix C GeoEASSData Read Parameter File Input Parameter File Pref ix Use this option to enter a prefix which is used to build file names save Parameter File used by the progran Output Parameter File Read Parameters Options Execute Save Parameters Quit Enter the Prefix for files Figure 12 1 Krige Main Screen The Main screen and menu for Krige shown in Figure 12 1 provides options to specify the file prefix to read or save program parameter values in a parameter file and to access the Krige Options menu where program parameter values are specified and kriging is initiated The menu line appears as follows Prefix Read Parameters Options Execute Save Parameters Quit Prefix The Prefix option is used to enter the prefix for the data file name Read Parameters The Read Parameters option provides a means of loading program parameter values froma parameter file When this option is selected a prompt is issued forthe Input Parameter File name A default name is constructed from the most recently used Geo EAS data file name using the file extension kpf krige parameter file Once the name has been specified the parameter file is accessed and the parameters are retrieved
107. executes the Variable option The program assumes that the X and Y variables are the first and second in the file respectively This is correct so you should accept both by pressing lt enter gt twice The program also assumes that the third variable is the one we want to post This is incorrect we want Cadmium not Arsenic so use the lt space gt key to toggk through the list of variables until Cadmium is found and then press lt enter gt Now use the Execute option it will move you to the metacode file name field Accept the default metacode file name Metacode met is effectively a permanent scratch file and wait for the plot to appear on the screen After examining the plot hit lt q gt to return to the main menu and use the Qut option to return to the system menu or DOS To simplify our explanations in the future an abbreviated notation for the above sequence of events will be used A general formula exists for each option initiate the option then take one or more actions each of which may result in a screen field taking a particular value The above sequence thus becomes OPTION ACTION FIELD VALUE DATA Enter Data File Example dat VARIABLE Accept x Easting Accept y Northing Select variable Cadmium EXECUTE Accept metacode file Mecode met lt Q gt QUIT Answer Y The resulting Post plot is shown in Figure 4 2 PGatplot L Cadmium from data file sxample dat 300 250 200 Northing 591 160 400 409 East
108. f neighbors A toggle field for selecting how many sectors in which to divide the search ellipse The choices available are 1 the default 4 and 8 The combination of the Number of Sectors and the Max Points per Sector parameters indicate the maximum number of samples to be used for kriging This parameter also serves to indicate the number of groups to use for classification of neighbors The search ellipse is divided into the chosen number of equally sized sectors If a sample is found to be within the search ellipse its sector number is stored These sector numbers and sample distances are used for elimination of samples which exceed the Max Pts Sector value A toggle field for selecting the maximum number of points which a sector may contain The choices range from 1 to a maximum which depends on the number of sectors chosen If one sector is specified up to 24 points neighbors may be used If four or eight sectors are selected the choices are constrained such that a maximum of 64 neighbors may be retained If the number of neighbors in a sector exceeds the specified value the farthest samples as determined by Distance Type are eliminated from consideration A toggle field for selecting the minimum number of neighboring samples to use for kriging The default value or this parameter is 1 If fewer than the specified number of samples are found then kriging is not performed and a missing value is generated for the est
109. f the direction parameters From this omnidirectional variogram we can usually get the best estimate of the y intercept nugget and maximum value sill parameters for the variogram model as well as the best idea of what type of model s should be fitted Next try several different lag intervals for plotting the experimental variograms You are trying to obtain the maximum detail at small distances i e small lags without being misled by structural artifacts due to the particular class interval used You will have more confidence in a model if it fits experimental variograms computed at several different lag intervals The default lag intervals are computed from a rule of thumb which states that variograms ar generally not valid beyond one half the maximum distance between amples The maximum pair distance is therefore divided by two and then subdivided into ten equal distance classes Round these to the more convenient numbers of 150 and 15 and plot the resulting variogram Figure 4 10 as follows OPTION ACTION FIELD VALUE NEW LAGS Accept Minimum 0 Input Maximum 150 Input Increment 15 EXECUTE PLOT lt Q gt Variogram for Cadmium Parameters File EXAMPLE pcf Pairs Direct Tol MaxBand f L fal S t A Bb Cadmium Limits Minimum Maximum Mean Var Distance Figure 4 10 Variogram of Cadmium This variogram shows a well defined structure Except for the fifth point which is too low
110. f the exponent e IF Exponent has a value less than or equal to zero P is omitted If Exponent is less than zero and has the integral absolute value n the fraction f is forced to have n leading zeroes The parameter fraction specifies the number of characters in f If Fraction is less or equal to zero f is omitted If Fraction is less than zero the decimal point is omitted If i f has the value 1 the first part of the label is omitted leaving only 10e If the entire label has the value 0 is used Exponent Labeling Setting Label to Expon selects exponential notation If the parameter Type has the value_Base k Each numeric label is written in the form i f 10e Where brackets enclose portions which may be independently present or absent and e is a Superscript exponent The parameter Exponent specifies the integral value of the exponent e The parameter Fraction specifies the number of characters in f If Fraction is less than or equal to zero f is omitted If Fraction is less than zero the decimal point is omitted If the label is exactly zero the single character 0 is used If the parameter type has the value_Base 10 k Each numeric label is written in the form G f 10e The parameter Exponent specified the integral value of the exponent e when K equals 0 The value of e is
111. f the graph is the lag number the number of pairs the variogram value the minimum and maximum distance used in computing the lag the direction tolerance and maximum bandwidth and the sample value limits An example lag histogram plot is displayed in Figure 10 8 Scatter The Scatter option allows you to view a lag scattergram This is a plot of pairs of sample values Every pair of sample values is represented as a point in the scatter plot where the X coordinate is the value of the first point in the pair and the Y coordinate is the value of the second point in the pair Points are plotted for all pairs in the lag subject to the limits criteria direction tolerance bandwidth sample value limits and interpair distance which have been specified Displayed on the right side of the graph is the lag number the number of pairs the variogran value the minimum and maximum distance the direction tolerance and maximum bandwidth and the sample value limits Figure 10 9 displays an example lag scattergram Lag Histogram for Cadmium T RT 10 Ep Paramete Lag Pairs Vario 15 MinDist 75 MaxDist 98 Direct Tol g8 MaxBand Cadmium Limits Minimum Maximum a N E U S u L amp 86 166 246 C202 2 xt h Squared Figure 10 8 Vario Lag Histogram Lag Scatter Plot for Cadmium Paramete Lag Pairs Vario MinDist MaxDist Direct Tol MaxBand Cadmium Limits
112. ge Lags option allows you to change the lag cutoff distances on the Options screen This provides a means of specifying unequal lag intervals The screen fields accessed from this option are a group of numeric fields for entering new lag cutoff values After these have been entered the program will sort the values by increasing distance and re display them if necessary Post Plot The Post Plot option allows you to view a post plot of the data This plot shows the actua locations of the sample points Each point is labeled with a character The X and Y axes are automatically scaled and labeled This graph is useful in determining the lag cutoff distances for the New Lags option Figure 10 4 displays an example post plot for Example dat Plot of sample locations a E H D Figure 10 4 Vario Post Plot Execute When the Execute option is selected the program displays the Results screen and computes the lag results before providing access to the Results screen and menu Figure 10 5 This menu is described below 10 6 THE RESULTS MENU RESULTS Variable Cadmium Direction Minimum Estimator z Variogram Tolerance Maximum Total Pairs 1388 BandWidth Type Box Plot Lag Results Model Quit Plot the selected estimator vs average distance Figure 10 5 Vario Results Screen The Results screen and menu Figure 10 5 has options to select the type of est
113. he More command The screen R cleared and the contents of the file are displayed When the screen is filled the message More appears on the last line The lt enter gt key causes another page of the file s contents to be displayed After the entire file has been listed press lt enter gt to display the List menu screen and control is returned to the List menu Copy Upon selection of this option the Copy menu is displayed The Copy menu provides the options necessary to copy a file The menu line appears as follows Files Execute Quit Files You are prompted for two file names Upon execution the contents of the first data file are copied over to the second data file Execute Upon selection of this option DOS executes the Copy command When the file has been copied a message is displayed An error message appears whenever the Copy command could not be successfully executed Rename Upon selection of this option the Rename menu is displayed The Rename menu provides the options necessary to rename a file The menu line appears as follows Files Execute Quit Files You are prompted for two file names The name of the file specified first is renamed to the second file name given If a data file exists with the second file name then an error message appears Execute Upon selection of this option DOS executes the Rename command A message stating that the file has been renamed appears after the process is complete De
114. he file an error message is generated If the variable names are loaded successfully the Krige Options menu will be re activated Output File A 14 character alpha numeric field for entering the name of the output file of gridded estimates A default name is constructed which consists of the input data file name with a grd extension signifying gridded data If the specified file already resides on disk a Yes No prompt provides the alternative of overwriting the file or exiting the option Polygon The Polygon option is used to specify the name of a file containing polygonal boundaries which limit the area in which estimates are produced This file should contain one or more lists of polygon vertices which form closed polygons For each block or point in the grid a FLAG is kept which indicates if the block estimate is to be excluded from computation When no polygon files is specified KRIGE sets all the flags to INCLUDE If a polygon file is specified all flags are initially reset ot EXCLUDE and then modidied sequentially by the coded polygons in the file The codes result in the following operations IF Code 0 Flags are set to INCLUDE blocks INSSIDE the current polygon Blocks outside remain unchaged IF Code 1 flags are set to EXCLUDE blocks INDIDE the current polygon Blocks outside remain unchanged IF Code 2 The flag settings are REVERSED for blocks INSIDE the current polygon Blocks outside remain unchanged IF Code
115. he maximum value exceeds the minimum value then an error message is displayed and the default value is the previous field entry The default values displayed ar determined from the data file for the variable for which univariate statistics are computed and from the upper and lower class limits Tic Spacing Two numeric fields used for entering the tic spacing to be used on the X and Y axes The default values displayed are determined from the data file for the variable for which univariate statistics are computed and from the upper and lower class limits Titles The Titles option allows you to enter the title and labels for the graph The Hershy character sets of 33 fonts are used for plotting alphanumeric labels The file HERSHY BAR contains ths information and is included with the software Main Title An alphanumeric field which may contain up to 60 characters for the title on the graph The default title is Histogram Whena weighting factor has been selected then the title is Weighted Histogram Subtitle An alphanumeric field which may contain up to 60 characters for the subtitle of the graph The default sub title is Data file lt input data file name gt X Axis An alphanumeric field which may contain up to 60 characters for the X axis The default label is lt variable name gt lt units description gt where the variable name and the measurements description are taken from the variable selected for univarnte statistics
116. he sum of two or more component models such as nugget spherical etc Adding a nugget component to one of the other models is the most common nested model but more complex combinations are occasionally used Aconstant variance model most often used in combination with one or more other functions when fitting mathematical models to experimental variograms In Geo EAS the kriging search neighborhood ellipse may be divided into eight equal angle sectors which may have minimum and maximum numbers of samples specified A limit on the number of consecutive empty sectors may also be specified When the specified criteria are not satisfied for a particular point or block then the kriged estimate is not produced A variety of kriging which assumes that local means are not necessarily closely related to the population mean and which therefore uses only the samples in the local neighborhood for the estimate Ordinary kriging is the most commonly used method for environmental situations Estimating the value of a point from a set of nearby sample values using kriging The kriged estimate for a point will usually be quite similar to the kriged estimate for a relatively small block centered on the point but the computed kriging standard deviation will be higher When akriged point happens to coincide with a sampled location the kriged estimate will equal the sample value In Geo EAS the kriging search neighborhood ellipse may be divided into four equal ang
117. her Geo EAS programs for a more detailed analysis of the pair information 10 8 THE VARIOGRAM MODELING MENU The Variogram Modeling screen and menu has options to allow you to specify the variogran model to display the graph options and to plotthe variogram estimates and the specified model This screen is displayed in Figure 10 11 The menu line appears as follows Model Plot Options Quit Pairs ug Distance Pairs Avg Distance 1 Z 3 4 5 6 7 8 9 996 837 114 330 717 650 726 411 538 869 Spherical Options Quit Figure 10 11 Variogram Modeling Screen Model The Model option allows you to edit or enter the parameters for the variogram model Up to four nested variogram structures and a nugget component can be included in the model The screen fields access from this option are Nugget Type Sill Range A numeric field for entering the nugget effect The value entered must be greater than or equal to 0 Four toggle fields used for selecting the type of variogram structure The choices available for each are Sphencal Gaussian Exponent Linear and 9 If is selected the structure will be ignored Four numeric fields for entering the sill for each structure Four numeric fields for entering the range of influence of the structure The range of the variogram structure The range in a spherical model is the distance at which the model curve becomes horizontal In a gauss
118. iable Northing Execute Variable to post Cadmiun Use this option to create the Opt ions plot The plot will be saved in Include Values No i the file specified Scale Factor 10 0 Decimals gt 1 Include Symbols 4 Prefix Data Variables Options Graph Options Quit Generate the plot Figure 4 1 PostPlot Main Screen XK NOTE Whenever feasible the programs will use default options and values These may be preset computed from the available data or passed from a previously run program Be careful The computer doesn t understand your problem or your data Defaults make it easy to get a result quickly not necessarily to get an appropriate result In this example we will usually use the defaults to get quick results Try other options to get familiar with the full range of system capabilities In Postplot the minimum that you MUST do to obtain a plot is 1 Use the Data option to enter the name of a Geo EAS data file or accept the default name if one is provided 2 Use the Variable option to select the X and Y variables and the desired variable for posting or accept defaults 3 Use the Execute option to enter a name for the metacode file or accept the default create the metacode file and display the map In this case you can skip the Prefix option because the data file is in the Geoeas directory and enter the file name Example dat with the Data option The program reads the data file and automatically
119. ian and exponential model the range parameter entered is a practical range at which the model attains 95 of its maximum value In the linear model the range and sill are used to define the slope of a linear structure The practical effect of this is that the model type can be changed without changing the apparent range of the model curve Plot The Plot option allows you to view a plot of the estimates with specified model superimposed An example plot is displayed in Figure 10 12 The distance is plotted along the horizontal axis and the variogram is plotted against the vertical axis The type of estimatr and the variable name is displayed as the graph title Vertical and horizontal axis scaling and tick mark spacing ae calculated by the program Displayed on the right side of the graph are the total number of pairs the minimum and maximum distances the direction tolerance and maximum bandwidth the sample value limits and the mean and variance of the sample values Press lt q gt to clear the screen and access the Variogram Modeling menu Variogram for Cadmium Parameters File Exanple pcf Pairs 1366 Direct Malala Tol HHH MaxBand naa E H S D H L gt Cadmium Limits Minimum Max imum Mean Var 80 Distance Figure 10 12 Plot of Variogram with Model Curve Options The Options option provides access to the Graph Options screen and menu displayed in Figure 10 13 10 9 THE GRAPH
120. igpitan Quit Specify variogram options compute Figure 4 8 Vario Main Screen The following option sequence reads the pair comparison file into memory ad moves to the next menu OPTION ACTION FIELD VALUE DATA Accept Pairs File Example pcf VARIABLE Toggle Variable Cadmium Accept Log Option Off OPTIONS EXECUTE The Options Execute menu allows us to specify how we want the experimental variogram to be computed This screen and menu is displayed in Figure 4 9 U PT LUN 2 Variable Cadmium Pair File gt Example pef Minimum 000 Min Distance Maximum 16 7 Max Distance Direction Direction Tolerance Max Bandwidth Lag Spacing 1 2 3 4 5 6 7 8 9 Minimum Maximum Increnent New Lags Change Lags Post Plot Execute Quit Specify pair orientation selection criteria Figure 4 9 Vario Options Screen First specify the distance class intervals lags and directional tolerances for computing the variogram Finding the right combination is a trial and error exercise but a systematic approach can be helpful To start you will use the default direction which is an omnidirectional variogram The angular tolerance of 90 degrees on either side of any specified direction line allows all pairs to be included regardless of direction This maximizes the number of pairs in each distance class which usually gives the best or smoothest variogram See Figure 10 3 in Section 10 for a more detailed illustration o
121. ile Demo1 dat was sorted Out4 dat Demol dat ficticious data set 1 3 Easting feet Northing feet Arsenic ppm 114 0 269 0 1 02 114 0 269 0 1 02 115 0 111 0 560 119 0 119 0 630 320 0 311 0 850 431 0 137 0 670 The variable Easting appears in ascending order Note that not only have the values of the variable Easting been relocated but all values the line associated with Easting has been moved SECTION 6 TRANS 6 1 WHAT TRANS DOES Trans was designed to create delete or modify Geo EAS data file variables Refer to the section on Geo EAS data files for more information on input data The operations may be unary one operand one operator binary two operands one operator or a indicator transform operation described below An operand may be either a variable or a constant The operator maybe an operation such as addition or finding the square root The results generated by the specified operation may replace the contents of an existing variable or a new variable may be created The variable specified to accept the results is called the result variable Missing values may be generated in two circumstances when an operand is a missing value or when an operation R undefined as in division by zero Trans uses a temporary file called a Scratch File to store the data read from a Geo EAS data file The temporary file is called ZZSCTCH1 FIL The Read option in the Main menu described below reads the Geo EAS data file
122. imate and kriging standard deviation Empty Sectors A toggle field for selecting the maximum number of consecutive sectors with no neighbors The choices available are determined by the Number of Sectors parameter If one sector is chosen then this input is ignored If more than the specified number of consecutive sectors are empty no value is kriged and missing values ate generated in place of an estimate and kriging standard deviation Variables Models The Variables Models option is used to access the Variables Models screen and menu Ths screen and menu are used for selecting the variables to krige and the variogram model to use for each variable Up to ten variables may be selected for kriging At least one must be specified prior to selection of the Execute option The Variables Models screen and menu is discussed below Title The Title option is used to indicate the descriptive title to store in the output file of gridded estimates It provides access to a 60 character alphanumeric field for storing the title A default title is constructed from the data file name and the output file name Any valid alphanumerr character string may be entered Execute The Execute option is used to initiate kriging All parameters must be specified before kriging may begin Several Debug Options described below are enabled or disabled with the lt caps lock gt the lt num lock gt and the lt scroll lock gt keys These keys are used to toggle
123. imator to be computed to view a variogram and box plots to recompute detailed results for a specific lag and to display the Modeling screen and menu The menu line appears as follows Type Plot Box Plot Lag Results Model Quit Type The Type option allows for the selection of the type of estimator to display and model Tle screen field accessed from this option is a toggle field The choices available are Variogram Relative Madogram and Non Ergodic The default is Variogram See the glossary for a definition of these terms Plot The Plot option allows you to view a variogram plot of the selected estimator The distance h is plotted along the horizontal axis and the variogram is plotted on the vertical axis The type of estimator and the variable name are displayed as the graph title Vertical and horizontal axes scaling and the tick mark spacing are calculated by the program Displayed on the right side of the graph are the number of pairs the lag minimum and maximum the direction tolerance and maximum bandwidth the sample limits and the mean and variance of the sample values An example graph is displayed in Figure 10 12 near the Plot option in the Modeling screen Box Plot The Box Plot option allows you to view a variogram boxplot displayed in Figure 10 6 This is a plot which displays statistical information about each lag The vertical lines represent the range of values in the lag with the minimum value at the
124. imum bandwidth The maximum bandwidth is the maximum perpendicular distance from the direction centerline to the second point in a pair The default value is MAX meaning that no such constraint is imposed An illustration of the function of the Lag Cuttoff Direction Tolerance and Maximum Band width parameters The pair P1 P will be included in the compu tation for Lagi The pairs Fi P2 and Pi P6 will be included in the computation for Lag2 X axis direction Figure 10 3 An Illustration of the Direction Parameters New Lags The New Lags option allows you to choose new pair distance intervals Pairs are included in a lag if the distance for the pair is greater than the previous cutoff value and less than the cutoff value for that lag The screen fields accessed from this option are Minimum A numeric field for entering the minimum inter pair distance The first lag wil contain pairs strictly greater than this value Maximum A numeric field for entering the maximum inter pair distance Increment A numeric field for entering the increment between lag cutoff values The defaults for these fields are calculated as Minimum 0 0 Maximum one half the maximum interpair distance and Increment Maximum divided by 10 0 These values may not be appropriate for the data configuration Once these parameters are specified the lag cutoff distances are displayed in columns on the Options screen Change Lags The Chan
125. ing Teat det Guortiles 00 4 2306 2nd Quartile 3 300 lt F 600 Ord Guortile 699 Z OF 10 8600 4th Guortile 10 500 16 700 Figure 4 2 Post Plot of Cadmium From this plot you can see that the samples fall in a rectangular area about 250 by 220 feet The sample locations are irregularly spaced and although there are some gaps and clusters they provide relatively uniform coverage over the entire rectangle The symbols colors represent the quartiles for the cadmium values with red as the upper quartile and blue as the lower A general trend can be seen in the cadmium values The highest values occur in a rough E W band through the center of the plot while the lowest fall in parallel bands at the north and souh margins The in the northwest corner of the area seems to be anexception to the trend it seems too high compared to its surroundings Such spatial outliers should be checked to confirm that their coordinates and data values are valid For this example you will assume that this sample is valid While the plot is on your screen you will note that there is no menu line at the bottom What do you do now Every graphics screen actually has two invisible options available lt p gt Print and lt q gt Quit which produces a screen dump on your printer and returns you to the man menu respectively xxx NOTE Don t try a screen dump if your printer is not connected and turned on the program will ha
126. ing is entered into an alphanumeric field that is 55 characters long If the field is left blank then the current directory is used by default Execute Selection of this option causes the directory to be displayed on a new screen An error message appears if the directory is non existent After the directory is listed the message Press lt enter gt to return to menu is displayed The lt enter gt key returns control to the Directory menu Print Upon selection of this option the Print menu is displayed The Print menu provides the options necessary to print a file The Print option is similar to the DOS command Print The menu line appears as follows Files Execute Quit Files Upon selecting this option you are prompted for the name of the file that is to be printed Execute Selection of this option causes the specified file to be printed A yes no prompt appears asking if the printer is ready If yes is indicated then the DOS Print command is executed When printing begins the Print menu screen is displayed and a message appears indicating that the file is being printed List Upon selection of this option the List menu is displayed The List menu provides the options necessary to list a file The List option is similar to the DOS command More The menu line appears as follows File Execute Quit File You will be prompted for the name of the file that is to be listed Execute Upon selection of this option DOS executes t
127. ion on the Results menu below for more information Batch Statistics The Batch Statistics option allows generation of a report of univariate statistics for all variables in the data set with no need for interaction The statistics can be saved to a file or printed A two valued toggle field printer or file is used to make this selection and appears on the message line If the selection is printer then the printer must be on and online If file is selected then you are prompted for a file name The field accepts up to 14 alphanumeric characters If the file exists then a yes no prompt asks if you wish to overwrite Indicating no will return you to the menu If the field is blank then an error message is displayed In such a case pressing any key returns you to the Main menu xxx NOTE the file by produced by the Batch Statistics option is not a Geo EAS data file 7 5 THE RESULTS MENU RESULTS Data File C NGeoEASNData Exanple dat Variable Cadmium Lower Limit 000 Upper Limit Observations Missing Data Retained i Sum of Weights 60 0000 Mean 7 8850 Minimum Value 0000 Variance 15 5315 25th Percentile 5 3000 Std Deviation 3 9410 Median 7 9500 Coeff Variation 49 9609 75th Percentile 10 8000 Maximum Value 16 7000 Skewness 1510 Kurtosis 2 4639 Probability Plot Examine Quit Choose histogram parameters lt display graph Figure 7 2 Statl Results Screen The Res
128. is a natural and convenient way of providing choices for program use The menu tree representation of progran options provides a road map for each program which summarizes the functional capabilities ofa program You may explore the hierarchy of options by traversing the menu tree and reading tle descriptive messages which appear 3 2 4 Common Menu Options Many of the programs in the Geo EAS system share common menu options These will be discussed in this section to avoid redundancy Any minor differences which apply to a particular program will be discussed later in detail The following is a list of options common to many programs Prefix This option is common to all Geo EAS programs It isused to specify a string of up to 50 alphanumeric characters which are used as a prefix for all files accessed by a program Typically it is used to include a disk drive and or a directory specification Before a file is accessed by a program a file name R constructed which consists of the File Prefix followed by the given file name File name errors are not caught by the programs until they have attempted to access a file Consequently file not found error messages are not issued until an attempt to access the file has been made This may be due to a mistake in the file prefix or file name specified Data This option is common to most Geo EAS programs It is used to indicate the Geo EAS input data file to be used by the program File names consist
129. is file Minimum Maximun Size Data Variables Graph Options Contour Options Quit View the contour plot Figure 15 2 Conrec Options Screen The Options screen and menu shown in Figure 15 2 has the options to allow specification of the data file name and the selection of variables to be used The menu line is as follows Data Variables Graph Options Contour Options Execute Quit Data The Data option is used to enter the data file name The file must have coordinate variables with values that form a complete grid An example of such a file is the file of kriged estimates produced by the program Krige Krige creates a file with a grd extension by default This is a Geo EAS data file which contains gridded data Variables The Variables option allows selection of the variables that are to be used as the X and Y coordinate values and the variable to be contoured The choices available are the variable names as specified in the data file If a grid could not be formed from the data an error message R displayed After the grid is formed a Yes No prompt is displayed which allows computation of defaults for the Graph Options and Contour Options screens If the response is Yes defaut values for Contour Options and Graph Options options will replace any previous entered values on these screens If the response is No and no contour levels have been set an error message will occur when the Execute option is selected The screen fields acces
130. iskettes The distribution diskettes contain the files needed for system operation Some programs require the presence of a character font file in order to execute properly Below is a list of the files which are included on the distribution diskettes Program files GEOEAS EXE DATAPREP EXE TRANS EXE STAT1 EXE SCATTER EXE PREVAR EXE VARIO EXE XVALID EXE KRIGE EXE CONREC EXE POSTPLOT EXE XYGRAPH EXE VIEW EXE HPPLOT EXE Miscellaneous files HERSHY BAR EXAMPLE DAT EXAMPLE GRD_ METACODE MET HPGL PLT HPSETUP BAT READ ME HPPS COM HPPS DOC HPPS ASM HPPSREAD ME the system menu program data management utilities data transformations basic univariate descriptive statistics scatter plots linear regression pair comparison computations for VARIO variogram analysis and modeling cross validation of parameters for KRIGE 2 dimensional kriging contouring of gridded data graphs of sample locations and values 2 dimensional line scatter graphs plots graph files on the screen creates plotter files from graphic metafiles character font file required by CONREC POSTPLOT XYGRAPH VIEW and HPPLOT example data file example gridded data file for CONREC example graph file example plotter instruction file commands to set up plotter communications additional last minute information screen dump capability for HP Laserjet document file for HPPS COM source file for HPP
131. istical software In the summer of 1986 as the authors were designing arelatively straightforward consolidation of this software involving standardization of parameters and file structures we were approached by Andre Journel and Roland Froidevaux of Stanford who enthusiastically demonstrated a prototype of a user friendly PC based geostatistical package written by Froidevaux in Turbo Pascal and recommended that we consider a similar approach Although this would considerably increase the scope of the effort the potential technology transfer value was very high and we decided to proceed A team consisting of Nancy Fisher of the Computer Sciences Corporation CSC Journel Froidevaux Flatman and the authors defined the philosophy and sketched the initial design for the system drawing heavily on Froidevaux s example for the look and feel of the menu driven user interface and integrated graphics It was decided among other things to program in FORTRAN to try to stay entirely in the public domain to use a simple ASCII data file structure and to target a hypothetical user with an AT and EGA graphics Suleiman Lalani of CSC provided a major boost to the software development by contributing the screen management software used throughout the package Chris Nisi of CSC coded the Dataprep and Trans programs Melissa Robinson of CSC converted public domain graphics routines from the National Center for Atmospheric Research NCAR an
132. kmark labels along the X and Y axes Choices available are Auto System will select appropriate format None No tick marks on axis Scien Scientific notation Expon Exponential notation No Exp Non exponential notation Fraction Two numeric fields for entering the number of significant digits to display in the numeric axis labels Exponent Two numeric fields for entering the value of the exponent in the numeric axis labels Table 13 1 shows examples of the types of numeric tick mark labels that can be produced using combinations of choices for the Base Type Label Fraction and Exponent parameters The labels were produced using the Example dat data file with Easting as the X variable and Northing as the Y variable Remember that certain combinations of parameter values are ncompatible and will result in unexpected results or a lack of tickmark labeling The Reset option may be used to set parameter values back to their defaults if this occurs Table 13 1 Numeric Tickmark Label Examples Graph Limits The Graph Limits option allows you to enter values that specify the coordinate limits for the X and Y axes Certain combinations of the Tick Parameters will cause these values to be overridden by tle program The screen fields accessed from this option are Min Two numeric fields for entering the minimum coordinate value to be used on the X and Y axes The default values displayed are determined from the variables selected as
133. le but it probable that other important contributing pairs will not be included The better approach would be b lt q gt uit and to select an interpair distance limit or coordinate limits to restrict the number of pairs computed SECTION 10 VARIO 10 1 WHAT VARIO DOES Vario is a two dimensional variogram analysis and modeling program Vario uses a par comparison file PCF produced by Prevar to calculate variogram values and other statistics for a specified set of pair distance intervals lags Tolerances may be specified for pair direction and lag distance intervals Plots of variogram values vs distance may be displayed Several graphs of the individual lag results may also be viewed such as lag histograms box plots postplots and lag scatter plots Variograms may be fitted with a model of up to 4 nested additive variogram structures Lag results for individual lags may be saved in a Geo EAS data file for analysis 10 2 DATA LIMITS Vario requires that the pair comparison file contains no more than 48 variables 1000 samples and 16384 pairs If there are more than 48 variables the data file may not be used If there are more than 1000 samples only the first 1000 will be used Up to 24 lag intervals may be defined As many as 2000 pairs may be used for an individual lag If more than 2000 pairs exist per lag only the first 2000 are used 10 3 THE MENU HIERARCHY Vario_____ Prefix Data Variable Limits Options Execute______
134. le sectors which may have minimum and maximum numbers of samples specified A limit on the number of consecutive empty sectors may also be specified When the specified criteria are not satisfied for a particular point or block then the kriged estimate is not produced For a spherical model the distance at which the model reaches its maximum value or sill For the exponential and gaussian models which approach the sill asymptotically Geo EAS uses range to mean the practical or effective range where the function reaches approximately 95 of the maximum The nugget model effectively has a sill with a range of zero the linear model uses sill range merely to define the slope A variogram in which the ordinary variogram value for each lag has been divided by the square of the mean of the sample values used in computing the lag This is sometimes useful when a proportional effect is present i e when areas of higher than average concentration also have higher than average variance When relative variogram models are used in kriging the resulting kriging standard deviations represent decimal fractions of the estimated values In Geo EAS an elliptical area centered on a point or block being kriged Only samples within the ellipse will be used for kriging When the next point is kriged the ellipse will be re centered and a different perhaps set of samples will be used Identical to the term variogram as defined in
135. le Prefix C GeoEASSData Input Parameter File Output Parameter File Options Use this option to select control parameters A menu of additional options will be displayed Prefix Read Parameters ISG Eg iasi Save Parameters Quit Edit or enter parameter values Figure 14 1 Xygraph Main Screen Prefix The Prefix option is used to enter the prefix for file names Read Parameters The Read Parameters option is used to enter the input parameter file name Options Execute The Options Execute option provides access to the Options screen and menu See the section on Options below for more information Save Parameters The Save Parameters option is used to enter the name of the output parameter file If the specified file already exists a Yes No prompt is provided to quit or proceed The parameter file will contain the current parameter values It will be saved for future use as an input parameter file 14 5 THE OPTIONS MENU The Options screen and menu Figure 14 2 has options to allow specification of the data and metacode file names the selection of variables to be used the options for displaying the variable to compute a regression line and the position of a graph legend The menu lire appears as follows Data Variables Symbol Line Regression Legend Graph Options Execute Quit OPTIONS Metacode File Metacode met Legend None Variables Syumbol Line Type X Variable Arsenic Execute Y Variables Symbol Type
136. le results in an undefined operation then a missing value is generated Whenever an error message R displayed processing is halted and control is returned to the Operation menu As noted previously the operation exp may result in a numeric overflow causing the program to abnormally terminate crash Binary Operation This option provides access to the Binary Operation menu The Binary Operation menu is the first of four menus that provides options needed to complete a binary operation After a selection is made from one menu control is passed to the succeeding menu First the Binary Operand One menu described below provides a selection of a constant or an existing variable for operand one Second the Binary Operation menu provides a selection of binary operators Next the Binary Operand Two menu is similar to the Binary Operand One menu with the exception that the selection is for operand two Finally the Execute menu provides the Execute option The binary operations perform an operation requiring two operands The operations are shown below as they would appear in the toggle field Addition Division of the first operand by the second operand x Multiplication Subtraction Exponentiation which raises the first operand to the power of the second operand MAX Determines the maximum value of the operands MIN Determines the minimum value of the operands Mean Computes the means of the operands The Binary
137. lete Upon selection of this option the Delete menu will be displayed TheDelete option uses the DOS command Del The menu line appears as follows File Execute Quit File You will be prompted for the name of the file to be deleted Execute Upon selection of this option DOS executes the Delete command After the file has been deleted an informative message is displayed DOS Command Upon selection of this option you will access DOS To return to Dataprep type the command Exit lt enter gt 5 6 THE FILE OPERATIONS MENU DATA PREPARATION 1 2 1 Data File Prefix gt C NGeoEASSData ss Scratch File Prefix FILE OPTIONS Rows of data ie samples are extracted from an input file based upon a logical Append expression and written to an output Column Extract file The first operand is a variable and the second operand can be either a Compress variable or a constant The logical ID Variable relations are LT LE GT GE Merge EQ NE Report The data file prefix noted above will sort precede the files Press lt enter gt Quit Figure 5 3 Dataprep File Operations Screen The File Operations screen and menu Figure 5 3 provides a set of useful operations f manipulating Geo EAS data files To select an option from the vertical menu use lt up gt or lt down gt not lt left gt or lt right gt to position the cursor and press lt enter gt to select the option The two Geo EAS input data files called Dem
138. m a Geo EAS data file and for processing The Append and Merge operations require an additional temporary file for processing The temporary files are called ZZSCTCHI1 FIL and ZZSCTCH2 FIL Each time an operation is executed the temporary files are generated and then deleted after processing is complete 5 2 DATA LIMITS Dataprep reads and generates Geo EAS data files containing a maximum of 48 variables and 10 000 samples If a file should contain more than 10 000 samples then only the first 10 000 samples are read and a warning message is displayed The file operations will generate output data files containing up to 10 000 samples If a file operation should generate an output data file requiring more than 10 000 samples then only the first 10 000 samplesare written In such a case no warning messages are displayed 5 3 THE MENU HIERARCHY Dataprep Prefix DOS Utilities Directory ___ _ File Operations Quit Print List _ Copy Rename _ Delete ___ _ DOS Command Quit Append _ Directory Execute Quit File Execute Quit File Execute Quit __ Files Execute Quit ____ Files Execute Quit File Execute Quit Files Execute Quit Column Extract____ Files Row Extract_ 2 Compress__ ID Variable __ Merge___ Report Sort Quit Variables Execute Quit Files Subsetting Condition Execute Quit Files Execute Quit Files
139. m value the class width and the number of classes The upper limit of the first class is the sum of the minimum value and the class width The upper limit for all classes is the sum of the minimum value and class width multiplied by the number of classes The screen fields accessed from this option are Minimum A numeric field whose default value is the minimum value which was specified in the Limits option of the Main menu discussed earlier Class Width A numeric field whose default value is calculated This value must be greater than zero If it is not then an error message appears and you are prompted for a new value Classes A numeric field for which the value entered must be in the range of 1 to 100 If the entry is erroneous then an error message appears and the default value is set to 100 Axes The Axes option allows the specification of the coordinate limits for the horizontal X and vertical Y axes Tic spacing for the X and Y axes is also specified at this time The screen fields accessed from this option are Minimum Two numeric fields used for entering the minimum coordinate values to be used on the X and Y axes The default value for X is determined from the data file for the variable for which univariate statistics are computed and from the upper and lower class limits The default value for Y is zero Maximum Two numeric fields used for entering the maximum coordinate values to be used on the X and Y axes If t
140. me of a valid metacode file or an error is displayed This file contains the metacode instructions produced by the programs Conrec Xyegraph or Postplot Scale The Scale option is used to select the type of plotting area to use when displaying the graph The screen field accessed from this option is a toggle field The choices available are Square the true scale of the graph and Rectangle the entire screen The default is Rectangle Execute When the Execute option is selected you will be prompted for a output file name before the output file is created The output file name entered must be up to 14 characters This fik contains the instruction generated by translating the metacode file into HPGL plotting instructions If a problem occurs while accessing the metacode file an error message is displayed When execution is complete the plot instruction file produced by Hpplot may be sent to an HP plotter or compatible This is accomplished by first running the DOS command fik HPSETUP BAT provided with the software distribution to configure the COM 1 serial port and redirect printer output to COM1 Type HPSETUP lt enter gt The file may then be sent to the plotter by using the DOS command PRINT Filename lt enter gt APPENDIX A REFERENCES Clark I 1979 Practical Geostatistics Applied Science Publishers London David M 1984 Geostatistical Ore Reserve Estiimation Elsevier Amsterdam Isaaks E H and Srevasta
141. ment Units The lines following the number of variables must contain the names and the measurement units for each variable 1 line per variable The variable name must be the first 10 characters in the line and the units optional must be characters 11 20 When a data file is accessed by a program the variable names are stored into toggle fields This allows one to select variables by name and provides some internal documentation of data fik contents Variable names will be used as default labels for graph axes in graphic displays Optional Fortan F format statements may be added in columns 21 to 30 in the Variable name records in a Geo EAS data file Programs such as TRANS and KRIGE which create new Geo EAS output files can use these to provide easier to read files The format statement is in the form Fx y where x is the total number of columns required by the variable including decimal point and minus sign if appropriate and y is the number of digits to be printed to the right of the decimal TRANS will add a blank space between variables For example F6 2 will allow printing of any number in the range 99 99 t 999 99 Line NVAR 3 To End of File the Data Matrix This is where the data are stored Columns represent variables and rows represert samples The data may be in free format which means that in a given line in the file variable values must be separated by at least one space or a single comma Far readability columns
142. mum and maximum values of the variable will be displayed on the message line After pressing any key you are asked for the number of significant digits for the output format The range of digits is 1 through 12 inclusive A FORTRAN format which is the output format is constructed based on the expression Gx 7 x where x is the digit entered by you ie significant digits For example if 7 is entered then G14 7 is the output format For more infomation on the FORTRAN formats refer to a FORTRAN reference manual If the digit for x is outside the acceptable range then 9 will be used by default If the given format is not appropriate for writing the variable to the output file then a message is displayed and you are prompted for a new digit for x You can best select x by determining using the minimum and maximum values displayed on the message line the maximum number of digits to the left of the decimal point Then decide the maximum number of digits to the right of the decimal point The sum of the two values is x Increase the sum by one if the value is negative If any missing values are generated then the number missing values and the name of the variable are displayed on the screen After processing R complete control is returned to the Main menu If an operand is a constant and contains a missing value then the result of that operation will be a missing value If the operand is a variable as opposed to a constant and a sample from that variab
143. n the X and Y axes The screen fields accessed from this option are X Tickmark Spacing Y Tickmark Spacing Limits A numeric field for entering the spacing between the X axis tickmarks A numeric field for entering the spacing between the Y axis tickmarks The Limit option allows you to specify the limits for the X and Y axes The screen field accessed from this option are X Axis Minimum X Axis Maximum Y Axis Minimum Y Axis Maximum A numeric field for entering the minimum coordinate value to be used on the X axis The default value is zero A numeric field for entering the maximum coordinate value to be used on the X axis The default value is the maximum distance calculated by the program A numeric field for entering the minimum coordinate value to be used on the Y axis The default value is zero A numeric field for entering the maximum coordinate value to be used on the Y axis The default value is the maximum variogram value calculated by the program SECTION 11 XVALID 11 1 WHAT XVALID DOES The name Xvalid stands for cross validation Cross validation involves estimating values at each sampled location in an area by kriging with the neighboring sample values excluding the value of the point being estimated The estimates are compared to the original observations in order to test if the hypothetical variogram model and neighborhood search parameters wil accurately reproduce the spatial variability
144. ng i x N Z at ls Deu N 18 276 119 7 24 3 33 3 41 it Figure 11 4 Xvalid Kriging Display Debug The Debug option is provided on the menu as a means of identifying the keys used for enabling or disabling the Debug displays This option does not actually do anything but moving the cursor bar to this menu option will display the Debug display names and the corresponding lt ___ lock gt keys which are used to activate them These displays provide a means of looking at intermediate kriging results during the cross validation process If the lt num lock gt lt caps lock gt or lt scroll lock gt keys are activated during kriging the corresponding displays will be generated on the screen To continue to the next display lt q gt is pressed To disable the generation of such screens the corresponding keys should be de activated On an IBM AT style keyboard these three keys are accompanied by status lights which indicate that the key is on or off Refer to the section on program Krige for a detailed discussion of the debug displays How to Cancel Kriging At any time during the kriging process kriging may be cancelled by pressing the lt ctrl gt and lt alt gt keys the lt ctrl gt and lt shift gt keys or the lt left shft gt and lt right shft gt keys simultaneously and holding them down until the next point has been kriged If this is done a message is displayed indicating that kriging has been terminated This is useful when the d
145. ng up and you will have to re boot with lt ctrl gt lt alt gt lt del gt Now you should use program Statl to generate some statistics on the data When Sati R initiated the Main screen will be displayed as in Figure 4 3 1 2 1 A program to compute univariate descriptive statistics File Prefix geoeas File Data File Name example dat Variable Variable Cadmium Weight None Log Option Off Limits Minimum Maximum Prefix Data Variable Limits Compute basic descriptive stats Figure 4 3 Statl Main Screen Variables g 5 Data records pH Missing Data H 2 Obs lt 8 Execute Use this option to compute and display the statistics A menu of additional graphs and options will be displayed Batch Statistics Quit The option sequence below is the minimum required to compute univariate statistics and display a histogram and a probability plot for the variable Cadmium Note that a default file name Example dat has been carried forward from the previous program When you finish examining the histogram you do not go directly back to the main menu an intermediate menu lets ya select alternate options for replotting the histogram COMMAND ACTION DATA Accept VARIABLE Select Accept Accept EXECUTE HISTOGRAM lt Q gt QUIT PROB PLOT lt Q gt VALUE Example dat Cadmium None Off The univariate statistics histogram and Probability plot are generated Figure 4 4 displays
146. nge the contour labels or specify unequal contour level spacing The screen fields accessed from this option are Contour Level A column of numeric fields for entering the contour levels Contour Label An column of 16 character alphanumeric fields for entering the contour labels Labeling The Labeling option allow you to select the contour labeling options The screen fields accessed from this option are Labeling Option A two valued toggle field to enable or disablethe labeling of contour lines The choices available are On label contours or Off do not label contours If the Labeling Option is Off the other screen fields in this group are ignored The default is On Label Skip Factor A toggle field for selecting the skip factor for the contour labels The Label Skip Factor is the frequency at which to label the contour lines For example if the Label Skip Factor is two and the First Level to Label is 1 then contour levels 1 3 5 would be labeled The choices available are 1 to 5 The default is 2 First Level to Label A ten valued 1 10 toggle field for selecting the first contour level to label The default is 1 Label Size A ten valued toggle field 1 10 for selecting the contour label character size The default is 6 Dash Pattern The Dash Pattern option allows specification of the Dash Pattern and the Dash Cutoff level The screen fields accessed from this option are Dash Pattern An al
147. ns menu The File Operations menu provides the following file operations Append Column variable extract Row extract Compress ID Variable Merge Report and Sort The File Operations menu is discussed below 5 5 THE DOS UTILITIES MENU DATA PREPARATION 1 2 1 Data File Pref ix gt C NGeoEASSData s Scratch File Prefix DOS UTILITIES The directory specified will be displayed You will be prompted for Directory the directory including the prefix Print if any Upon execution that List directory will be displayed on the Copy screen Press lt enter gt Rename Delete DOS Command Quit Figure 5 2 Dataprep DOS Utilities Screen The DOS Utilities screen and menu Figure 5 2 provides commonly used DOS commands These commands operate just as the DOS commands do Refer to your DOS manual for further information To select an option from the vertical menu use the lt up gt or lt down gt arrow key not the lt left gt or lt right gt arrow key to position the cursor bar then press the lt enter gt key Directory Upon selection of this option the Directory menu is displayed The Directory menu provides the options necessary to list all directory entries or only those for specifiedfiles The directory option is similar to the DOS command Dir The menu line appears as follows Directory Execute Directory This option results in a prompt for a character string The string can be eithera directory or file name The str
148. ntroductory screens This record contains the characters INTRO ON To disable the introductory screens use a text editor such as IDLIN to change the ON to OFF 3 2 INTERACTIVE SCREENS 3 2 1 Screen Format All Geo EAS programs have similar interactive features Each program uses interactive screens for selection of program options and display of results The screens are composed of several common components Figure 3 1 displays an example interactive screen from program Statl Below is a description of the common components STAT1i 1 2 1 A program to compute univariate descriptive statistics Pref ix C GeoEASSData Variables 5 Data records 64 File Name example dat Missing Data H 2 Obs lt 8 Variable Variable Cadmium Execute Weight None D Log Option Off Use this option to compute and display the statistics A menu Limits of additional graphs and options will be displayed Minimum Maximum Prefix Data Variable Limits Batch Statistics Quit Compute basic descriptive stats Figure 3 1 Example Interactive Screen A The Screen Frame This is the large double line rectangle which encloses each screen Program inputs and results ate displayed in this area Typically the screen frame is subdivided into smaller single line rectangles Each of these smaller rectangles contains a functionally related group of one or more input parameters or program results B The Message Line This is the dou
149. oEass Datas Scratch File Prefix Input File example dat Output File Title Example dat Geostatistical Environmental Assessment Software See D Variables East ing Northing Arsenic Cadmium Lead Prefix MAG Title Create U Delete Save Quit You will be prompted for an input filename Figure 6 1 Trans Main Screen The Main screen and menu Figure 6 1 provide the options necessary to read and save Geo EAS data files and to create delete or modify variables The menu line appears as follows Prefix Read Title Create Delete Save Quit Prefix The Prefix option is used to enter the prefix for the data file and scratch file Data The Data option is used to enter the name of a Geo EAS data file Title The Title option is used to specify a descriptive title for the output Geo EAS data file The title can be up to 66 alphanumeric characters No error checking is performed Create The Create option provides access to the Create menu The Create menu described below is the first in a series of menus that provide options used to specify a new or existing variable as the result variable and to perform a specified operation unary binary transform indicator Delete The Delete option is used to select an existing variable that is to be deleted The variable b selected from a toggle field Upon making the selection the message Do you really want o delete this variable CY N is displayed If lt Y gt is pressed the v
150. of numbers should line up although this is not required Variable values must be numeric with no embedded blanks In many cases several variables may be present in a data set but for some reason a value could not be obtained for a particular variable in a particular sample A special value may be given to the variable in this sample which will indicate to a program that the value is missing so that it will not be used in calculations The special value reserved for this is 1 E31 This is scientifi notation for a 1 followed by 31 zeros If your data set has mising values be sure to type a 1 E31 where the real value would have appeared Below is a portion of the fik Example dat It contains 5 variables and 60 samples Example dat Geostatistical Environmental Assessment Software 5 Easting feet Northing feet Arsenic ppm Cadmium ppm Lead ppm 288 0 311 0 850 11 5 18 25 285 6 288 0 630 8 50 30 25 273 6 269 0 1 02 7 00 20 00 280 8 249 0 1 02 10 7 19 25 273 6 231 0 1 01 11 2 151 5 276 0 206 0 1 47 11 6 37 50 285 6 182 0 720 7 20 80 00 288 0 164 0 300 5 70 46 00 292 8 137 0 360 5 20 10 00 3 1 2 File Naming Conventions Only valid DOS file names will be accepted by the programs For more information on DOS file names refer to the DOS reference manual All file names used by the Geo EAS programs are associated with a File Prefix The File Prefix provides a means of specifying a drive or subdirectory where data files should be acce
151. ogram Vario to calculate variogram values Limits may be imposed on the X and Y coordinate values or on the distance between points in a pair If no limits are specified all sample points are used for calculation The pair comparison file can become quite large if there are many points in the data file If is recommended that some limits on the distance between points be specified 9 2 DATA LIMITS Due to the storage requirements of Vario Prevar must impose limits on the number of sample points in the input file and on the number of pairs for which distances and directions ae computed The input data file may contain up to 1000 samples and 48 variables If more than 48 variables exist the data file may not be used If more than 1000 samples exist only the first 1000 will be used If there are N sample points in an input data file and no limits were imposed N N 2 inter pair distances and directions would be computed A file with several hundred samples would easily generate too many pairs for Vario The Limits option is used to restrict the number of pairs computed Prevar will compute a maximum of 16384 pairs 9 3 THE MENU HIERARCHY Prevar ____ Prefix Files Variables Limits Execute Quit 9 4 THE MAIN MENU FREVAR 1 2 1 A preprocessor for program VARIO File Prefix C GeoEASNDatas Files Variables 5 Data File Example dat Records 60 Pair Comparison File Example pcf Pairs possible 1770 Max 16384 Variables Fraction 1 000 Seed
152. ol dat and Demo2 dat areused to demonstrate each file operation discussed below Demol dat ficticious data set 1 3 Easting feet Northing feet Arsenic ppm 320 0 311 0 850 119 0 119 0 630 115 0 111 0 560 114 0 269 0 1 020 114 0 269 0 1 20 431 0 137 0 67 Demo2 2 dat ficticious data set 2 3 Easting feet Northing feet Lead ppm 102 0 164 0 300 122 0 137 0 360 116 0 119 0 700 150 0 315 0 500 148 0 291 0 710 Append Upon selection of this option the Append menu will be displayed The Append menu provides the options necessary to append two Geo EAS data files A discussion on the append operation follows in the Execute option The menu line appears as follows Files Execute Quit Files You are prompted for three Geo EAS data file names Upon execution the second fik name specified is appended to the first file name entered The first and second file names cannot be the same If they are then an error message appears The third file name entered is the name of the output file Execute Upon selection of this option Dataprep will append the second file to the first file and store the results in the output file After the operation is complete the output variables aie displayed on the screen and a message is displayed Upon pressing any key control is returned to the Append menu A discussion of the Append operation follows Assume the first input file will be called File1 and the second input file called File
153. ongest axis of the search ellipse A numeric field for indicating the length of the minor shortest radius of the search ellipse This value must be less than or equal to R Major non zero and non negative The default value is the value given forR Major If R Major is equal to R Minor the search area will be a circle A numeric field for indicating the orientation of the search ellipse It is given in trigonometric degrees in the range from zero up to but not including 180 and indicates the angle between the longest axis of the ellipse specified by R Major and the sample coordinate X axis IfR Minor is equal to R Major a circle search is used and the Angle parameter is ignored Distance Type Num Sectors Max Pts Sector Min Pts to Use A two valued toggle field for selecting the type of distance measure to use when eliminating neighbors The choices available are Euclidean the default and Variogram Neighboring samples are eliminated from consideration when the Max Pts Sector Maximum points per sector criterion is exceeded in a given sector If this should occur only the closest neighbors are kept If the Euclidean distance type is chosen neighbors are eliminated based upon the euclidean distance from the point to be estimated ellipse center If Variogram distance is chosen the variogram function value as specified by the Model parameters for the computed distance is used as the criterion for elimination o
154. or 0 03 This is not really bad but it might have been better to raise the maximum number of samples to 10 or 15 and increase the search radii if necessary The kriged results have been written to the file Example grd Proceed to contour this grid of kriged values using the program Conrec First initiate Conrec and use the following optim sequence The resulting graph is displayed in Figure 4 23 OPTION ACTION FIELD VALUE OPTIONS EXECUTE DATA Accept Data File Example grd Accept X variable Easting Accept Y variable Northing Accept Contour variable Cadmium Answer Y EXECUTE Accept Metafile Metacode met lt Q gt QUIT Keging egtrnatag produced From daba flies Exampla grd 240 Northing Contours for Cadmium Easting Figure 4 23 Contours for Cadmium Kriging Estimates The final option sequence below plots a contour map of the kriging standard deviations estimation errors Figure 4 24 and demonstrates some of the options in Conrec OPTION ACTION OPTIONS EXECUTE VARIABLES Accept Accept Accept Answer CONTOUR OPTIONS NEW LEVELS Accept Accept Input DASH PATTERN Input Input Accept QUIT EXECUTE Accept lt Q gt QUIT QUIT FIELD X variable Y variable Contour variable Starting Value Maximum Value Cont Increment Dash Pattern Dash Cutoff Rep Label Metafile VALUE Easting Northing KSDCadmium Y 1 3 0 25 1 9 5 Metacode met KeAging egtrnatag produced From daba fhe Exampla
155. ot be used A new data file name must be specified If no grid parameter values have been previously specified default values for the Origin Cell Size and Number of Cells parameters are computed Two numeric fields used for entering the X and Y coordinate values for the origin of the kriging grid If block kriging the default were selected the origin is taken as the center of the lower left hand grid block Two numeric fields for specifying the grid cell size For point kriging these values will indicate the distance between points in the grid For block kriging these parameters will indicate the size of the blocks to be kriged the distance between block centers in each direction Both values must be non zero and non negative Two numeric fields for selecting the number of points or blocks to be produced in each of the two directions These values must be non zero non negative and may not exceed 100 The Search option provides a means of controlling the neighborhood search used during kriging Parameters may be specified to define an elliptical search area Constraints may be placed upon the number of sectors and the number of samples to be retained in each sector of the search area and the type of distance measure to use when eliminating neighbors from a search sector The screen fields accessed from this option are R Major R Minor Angle A numeric field for indicating the length of the major radius half the length of the l
156. owered to the degree that its information is duplicated by nearby highly correlated samples This helps mitigate the impact of oversampling hot spots Anisotropy When samples are more highly correlated in a particular direction kriging weights will be greater for samples in that direction Precision Given a variogram representative of the area to be estimated kriging will compute the most precise estimates possible from the available data In practice this is only approximated as the variogram must itself be estimated from the available data Estimation of the variogram from sample data is a critical part of a geostatistical study The procedure involves interpretation and judgment and often requires a large number of trial and error computer runs The lack of inexpensive easy to use software has prevented many people from acquiring the experience necessary to use geostatistical methods effectively This software is designed to make it easy for the novice to begin using geostatistical methods and to learn by doing as well as to provide sufficient power and flexibility for the experienced user to solve real world problems EQUIPMENT REQUIREMENTS This system was designed to run under DOS Disk Operating System on an IBM PC XT AT PS2 or compatible computer Graphics capability is not required but is highly recommended as most programs will produce graphics output Graphics support is provided for the Hercules graphics card
157. phanumeric field which may contain up to 12 characters for entering Dash Cutoff Rep Label Annotation the line pattern to use for the contour line below the Dash Cutoff The Dash Pattern is a combination of characters and spaces with each non blank character representing a solid line segment in the Dash Pattern The default is The pattern would cause a solid line to be plotted A numeric field for entering the Dash Cutoff value If acontour level is below this value then the line is plotted using the specified Dash Pattern A toggle field for selecting the number of repetitions of the dash pattem between contour labels to plot Choices available are 2 to 10 The default is 5 The Annotation option allows the specification of the graph annotation The screen field accessed from this option are Annotation Option A toggle field for selecting the type of graph annotation for the graph The available choices are Plot Min Max and No Annotation do not plot the minimum and maximums The default is Plot Min Max If Plot Min Max is chosen the minima and maxima of the surface represented by the contour map will be plotted An H denotes a local maximum and an L denotes a local minimum Character Size A toggle field for selecting the character size to plot the graph Spline annotation Choices available are 1 to 10 The default is 8 This value works well on the screen however a sm
158. ple kriging If ordinary kriging is chosen this field is disabled and cannot be accessed The default value for the global mean is zero The following five fields are present for each of the four additive variogram structures Type A toggle field for indicating the type of the structure The toggle field choices for type are none Spherical Gaussian Exponential Linear The default type for all four structures is none If a structure is entered and the type is subsequently changed to none the structure will be deleted from the variogram model The order of the variogram structures on the screen is unimportant neither do they need to be ina contiguous order on the screen Delete Sill Major Range Minor Range Ellipse Angle A numeric field for entering the sill value for a variogram structure A non zero non negative value is required here If a linear variogram type is selected the sill value is used together with the variogram ellipse ranges to determine a slope for a given direction In a linear variogram structure the sill must be chosen so that the corresponding range parameter values will result in the desired slope A numeric value for entering the longest range of influence of the variogram structure The Major Range must be non zero and non negative This may be thought of as similar to the R Major parameter described in the Search option above In fact the variogram ellipse of influence is defined exactl
159. pomt at which to conclude that you have done the best you can given the quality and quantity of data The best remedy for this situation is practice Rerun KRIGE with Example dat using various combinations of the variogran model search strategy kriging type grid size etc until you get a feel for how these factors interact The two exercises below suggest ways of comparing the results from different kriging options and also utilize some of the other Geo EAS programs EXERCISE 1 Compare Anisotropic vs Isotropic variograms Step 1 Run Trans to read Example dat and write a new file named Compare dat Use the Create option to create a new variable Cd1 equal to the old variable Cadmium by adding a constant 0 to the variable Cadmium This step will help to avoid the problem of creating two kriged variables with the same name Repeat the process for another new variable Cd2 Delete the variables Arsenic Cadmium and Lead and save the result in Compare dat Step 2 Run Krige with the data file Compare dat to create a file of kriged estimates called Compare grd Krige both variables Cd1 and Cd2 in the same run Krige Cd1 with the anisotropic exponential variogram model you just used in the example Krige Cd2 with the equivalent isotropic model major and minor ranges both equal 160 Step 3 Run Trans with the grid file Compare grd to create a new variable called Cd1 Cd2 Save the results back into Compare grd Step 4 Run Conrec with the
160. puter See the section on Error and Recovery Procedures for more information 3 3 2 Metacode Based Graphics Postplot Xygraph and Conrec also plot graphics on the screen but only after writing a metacode file A metacode file is a file of device independent plotting instructions These files can be used later redisplay the graph on the screen or to plot it on a pen plotter Internally in these programs the metacode is written by a set of public domain FORTRAN subroutines produced at the National Center for Atmospheric Research NCAR in Boulder CO by their Scientific Computing Division These files are used by special translator programs called metacode translators which convert the metacode into device specific graphics commands Currently only two metacode translators are provided Program View translates metacode into video graphics for EGA CGA and Hercules graphics hardware and program Hpplot will convert metacode into HPGL Hewlett Packard Graphics Language plotting instructions Each metacode producing program uses a version of view to display the graphs during an interactive session Since producing and translating metacode takes longer than sending graphic commands directly to the display these programs take longer to draw graphs than thenon metacode producing programs The advantage to using metacode is the capability of obtaining higher quality graphic output on a pen plotter or other graphics device 3 4 ERROR AND RECOVER
161. r entering the nugget value for the variogram model Only values greater than or equal to zero may be entered The defaut value is zero Global Mean a numeric field for specifying the global mean for simple kriging If ordinary kriging is chosen this field is disabled and cannot be accessed The default value for the global mean is zero The following five fields are present for each of the four nested variogram structures Type a toggle field for indicating the type of the structure The toggle field choices for type are none Spherical Gaussian Exponential Linear The default type for all four structures is none If a structure is entered and the type is subsequently changed to none the structure will be deleted from the variogram model The order of the variogram structures on the screen is unimportant neither do they need to be ina contiguous order on the screen Sill a numeric field for entering the sill value for a variogram structure A non zero non negative value is required here In a linear variogram structure the sill must be chosen so that the corresponding range parameter value s will result in the desired slope s the actual model continues to increase indefinitely with distance Major Range a numeric value for entering the longest range of influence of the variogram structure The Major Range must be non zero and non negative This may be thought of as similar to the R Major parameter described in th
162. re attached and online or that disk drives have the correct density media and are ready for read write opeerations when Read Save or Write options are selected The following actions are guaranteed to create a lock up situation Trying to print a text or graphics screen when the printer is not connected or on line If a printer R connected make sure it is turned on and is ready to accept output from the computer on line If no printer is connected to your system you may have to re boot the computer in this case you shout avoid trying to print a text or graphics screen in the first place Accessing a file on a floppy deskette drive when the disk drive door is open or no diskette is present In some cases DOS may respond with a message Device no Ready Abort Retry Ignore Inserta diskette and press lt r gt for Retry If this does not work you must re start the computer SECTION 4 USING Geo EAS IN A GEOSTATISTICAL STUDY AN EXAMPLE 4 1 OVERVIEW This section will demonstrate how to use Geo EAS software to conduct a geostatistical study Starting with an example data set from a hypothetical pollution plume you will work through a complete study using many of the Geo EAS programs in the process Of necessity this exercise will be somewhat abbreviated We will conduct a relatively straightforward study illustrating the options which are likely to be most commonly used The data set example dat has bem included with
163. riograms the exponential model will be used At this point in the structural analysis anisotropy is the major remaining question When you looked at the post plot of the data there appeared to be a tendency for similar values to fom elongated E W bands Now you want to see if directional variograms confirm this effect Like lag spacings directions and angular tolerances require a trade off between resolution and precision If you plot four directional variograms at angles of 0 45 90 and 135 degrees with a tolerance of 22 5 degrees you have effectively divided the pairs in our omnidirectional variogram into four subsets This causes an increase in noise comparable to reducing the lag spacing by a factor of four It is therefore advisable to use a larger lag interval for computing directiond variograms You should use a lag spacing of 25 to compute the four directional variograms listed above superimposing the omnidirectional exponential model on the plot Run the optim sequence below four times changing only the direction angle Figures 4 16 through 4 19 display the directional variograms for 0 45 90 and 135 degrees OPTION ACTION FIELD VALUE QUIT QUIT DIRECTION Input Direction 0 Input Tolerance 22 5 Accept Bandwidth MAX EXECUTE MODEL PLOT lt Q gt Variogram for Cadmium E L H S D st H m gt 86 1268 Distance Figure 4 16 Variogram Exponential Model Direction 0 Parameters File Examp le pct Pairs
164. rmat for data files Note the term Data File is used to denote a specific type of file used by Geo EAS programs as opposed to Pair Comparison files Parameter files or Metacode files Data files are simple ASCII text files which may be created with any text editor It is importart to be familiar with this format and to make sure your data files are compatible or the programs will not be able to read them An example data file has been included with the distribution diskettes It is called Example dat Below is an explanation of the data file format Line 1 Title This line is a descriptive title which may contain up to 80 characters Most programs display the title on the screen when the file is read into memory Some programs will use the title as the default title for graphics screens Line 2 Number of Variables NVAR This line tells the programs how many variables are in the data file The data are stored in rows and columns where each column contains a different variable or measured quantity and each row represents a different sample location time etc The data file may hold up to 48 variables columns Different programs have different limits on the number of samples rows which can be read Typically upto 1000 samples may be read If a program encounters more than its limit of samples the remaining samples will not be read into memory and will not be used for computation Line 3 to NVAR 2 Variable Names and Measure
165. rol the format of the labels The default values are initially set to Auto and provide adequate labels for most data With the appropriate selection of parameter values however many useful labels may te constructed including fractions and superscripted powers of ten An excerpt from the NCAR documentation on tickmark parameters is included in the appendices Certain incompatible combinations of parameter choices will result in no labels being plotted or error messages generated by the NCAR Autograph utility These errors will cause the program to terminate To recover restart and change the parameters A menu option is provided to reset these parameters to Auto so that the default values may be used The screen fields accessed from this option are Base Two numeric fields used for the computation of major tick marks along the X and Y axes The user may accept the default value of Auto which allows the system to select the appropriate value or enter a value appropriate for the variable selected Type Two toggle fields for selecting a formula for computing using Base entered above the spacing of the tick marks along the X and Y axes Choices available are Auto System will select appropriate computation None No tick marks on axis Base k Base 104k Base k Note k is an arbitrary integer computed by the program The default value is Auto for both axes Label Two toggle fields for selecting the format of numeric tic
166. ror Map option described above An example plot is displayed in Figure 11 7 Scatter Plot Cross Validation for Cadmium Ff q L E a U S W q S 1 N Me Cadmium Figure 11 7 Xvalid Scatter Plot Histogram The Histogram option provides a histogram frequency distribution graph of the estimation error An example plot is shown in Figure 11 8 Histogram class intervals are computed automatically by the program A box plot of the differences appears at the top of the graph Descriptive statistics are displayed to the right of the histogram Histogram Estimated Variable Cadmium T R E Statisti N Total N Miss N Used Mean Std Dev Minimum 25th x gt Median Toth 2 gt Maximum a WW E 0 S a y H amp 4 D 4 Difference Estimate Cadmium Figure 11 8 Xvalid Error Histogram Write The Write option is used to store the result to a Geo EAS data file When this option is chosen a prompt for the file name appears on the message line If the specified file exists a Yes No prompt will provide an option to overwrite or quit If any errors occur while saving the results to the file appropriate error messages will be displayed on the message line If results were successfully saved a message will be displayed and pressing any key will re activate the Results menu The file created by this option contains seven variables Thefirst three are the t
167. rs Quit Enter the Prefix for files Figure 15 1 Conrec Main Screen The Main screen and menu Figure 15 1 has the options to allow specification of the input and output parameter file names The menu line appears as follows Prefix Read Parameters Options Execute Save Parameters Quit Prefix The Prefix option is used to enter the prefix for file names Read Parameters The Read Parameters option is used to enter the input parameter file name Options Execute The Options Execute option provides access to the Options menu See the section on Options below for more information Save Parameters The Save Parameters option is used to enter the name of the output parameter file The default output parameter file name is the data file name with a cpf extension If the file specified already exists a Yes No prompt for whether or not to overwrite the file is displayed This file will contain the current parameter values It will be saved for future use as an input parameter file 15 5 THE OPTIONS MENU CONREC 1 2 1 A contouring program for gridded data File Prefix C GeoEASSData Input Parameter File Data File Name Exanple grd Output Parameter File X Variable Easting Y Variable Northing Contour Variable Cadmium Use this option to View the graph The plotting instructions will be saved in a special file called a Graph Limits Metacode File Other software may be used to produce plotter Pts hardcopy from th
168. s The first operand is an existing variable and the second operand is a constant called the threshold value The result variable takes on the value 1 0 if the input variable is greater than or equal to the threshold value The result variable takes on the value 0 0 if the input variable operand is less than the threshold value The Indicator Transform option provides access to the Indicator Transform menu The Indicator Transform menu provides the options to select the operands and to execute the operation The menu line appears as follows Variable Execute Quit Variable This option is used to specify two operands The first operand is an existing variable and the second operand is the threshold value which is a constant The message Select variable for operation use lt space gt bar prompts for the variable After selection and pressing lt enter gt the message Enter constant value for threshold value is displayed If the constant entered causes numeric overflow then an error message is displayed Execute This option is used to initiate the indicator transform operation During processing the message Processing data is displayed Ifafter processing any missing values were generated then the number of missing values and the variable name are displayed on the message line After processing is complete the message Processing is complete press any key is displayed Upon pressing any key control is returned to the Main menu S
169. s The following is a list of commonly used keys Geo EAS 1 2 1 SYMBOL lt enter gt lt esc gt lt a gt lt Z gt lt 0 gt lt 9 gt lt ins gt lt del gt lt home gt lt end gt lt pg up gt lt pg dn gt lt left gt lt right gt lt up gt lt down gt lt backspace gt lt ctrl gt lt alt gt lt shift gt lt caps lock gt lt num lock gt lt scroll lock gt vii DESCRIPTION enter key escape key alphanumeric keys numeric keys insert delete keys page control keys cursor control keys backspace key special purpose keys Abbreviations ACKNOWLEDGEMENTS This document is intended to serve both as an introduction to the Geo EAS software package see Geo EAS Availability Section 1 3 and as a reference manual The Geo EAS software itself is of course the primary product and deserves a brief description of how it came about along with an acknowledgement of the many people who contributed to its development The ongoing USEPA research program in environmental geostatistics at the Environmental Monitoring Systems Laboratory Las Vegas EMSL LV was begun about six years ago largely through the efforts of George Flatman As an incidental result of various research projects conducted under Cooperative Agreements with Stanford University the University of Wyoming and the University of Arizona EMSL LV acquired a miscelleneous collection of public domain geostatistical and stat
170. s Style which consists of two toggle fields The choices available are Half left and bottom axes only Full left right top and bottom axes and Grid the same as Full but the major tickmarks extend across to the opposite axis The Axis Style for the axes are independent of each other for example if the Axis Style is Half for the X axis and Full for the Y axis the Bottom Left and Right axes would be drawn The default value is Full for both the X and Y axes Tick Parameters The Tick Parameters option allows the specification of the spacing and format of the numeri tickmark labels on the X and Y axes The screen fields accessed from this option are Major Tickmark Divisions Two numeric fields for entering the number of major tickmark divisions along the X and Y axes The default may be calculated by the program when the Variables option is selected Minor Division Major Two numeric fields for entering the number of minor tickmark divisions per major division along the X and Y axes The default may be calculated by the program when the Variables option is selected Tickmark Label Format An alphanumeric field which may contain up to 10 characters for entering a FORTRAN format specifier which describes how the label is to be printed The format must a valid FORTRAN format for a REAL value with a format width no greater that 10 A default format is constructed from the grid coordinate values This format should be adeq
171. s used to specify two file names the input and output files After the fik names have been entered you are prompted for the sequence option from thetoggle field If on is selected for the sequence option then the observation row number is indicated on the Report listing Variables This option is used to specify those variables that are to be included in the Report listing You are prompted for a variable to be selected from a toggle field A yes no prompt provides an opportunity to select another variable Indicating no causes control to be returned to the Report menu The list of variables are displayed on the screen after each selection Execute The Report listing will be generated upon selection of this option This listing is then stored in the specified output file When this operation is complete a message appears indicating that the data have been sent to the output file Upon pressing any key control is returned to the Report menu The following is a description of the Report listing The Report listing can be generated with or without the sequence option enabled If the sequence option is enabled then each data record will be preceded by an observation numba record number Each page lists up to four variables with 50 data recordseach If more than four variables are selected then all the data records for the first four variables are printed The page numbering is reset to one and the next four variables are printed An ex
172. screen a summary linefor each estimate is displayed As you watch this proceed you may note that the number of samples being used is only less than the specified 8 for the exterior blocks of the grid indicating that the default search radii are adequate to obtain 8 neighbors You can use the debug options during the kriging computations to help you understand what is actually happening in the program and to decide whether you need to change the search options Activating lt caps lock gt provides you with a map showing the search ellipse and the samples selected for kriging the current block The goal of the search is to include all of the samples which are relevant to the estimate while avoiding spending a lot of time computing negligible weights for samples that do not matter The lt num lock gt key lets you look at a list of the selected samples coordinates distances from the block center and kriging weights Use lt enter gt to continue to subsequent displays Given that sample weights must sum to 1 0 it seems reasonable to conclude that samples with weights of less than 0 01 can be neglected without significantly affecting the kriging results The goal of your search would therefore be to consistently find a set of samples such that the lowest two or three weights would be at or just below 0 01 When you examine the lists of weights for a number of blocks during this run you find the lowest weights to generally be in the range of 0 02
173. screen and menu described below Execute When the Execute option is selected you are prompted for a metacode file name The metacode file is then created and the graph is displayed The metacode file name entered may contain up to 14 characters The default value is METACODE MET or the name specified in the input parameter file If the file name is not METACODE MET and the file specified already exists a Yes No prompt provides the option to quit or proceed The metacode file is saved on disk for future viewing An example plot is displayed in Figure 14 4 A hard copy of the graph can be obtained by using the program Hpplot and an HPGL compatible plotter After the graph has been displayed type lt q gt to clear the screen and return to the Options menu Example dat Geoestotistical Environmental 4Assesesment Softwa CED 2 Serrelatien PPI ent 4 S Figure 14 4 Example Xygraph Plot GRAPH OPTIONS Axes Paraneters Tick Parameters Axis Style x Graph Limits Base Auto xX Y Type uto Min 000 1 000 Label Auto Max 5 610 302 500 Fraction Auto Scale Linear Linear Exponent Auto Titles Labels Main title Example dat Geostatistical Environmental Assessment Softwa Subtitles X Label Arsenic ppm Y Label Lead ppm Tick Parameters Graph Limits Title Labels Reset Quit Select style for X and Y axes Figure 14 5 Xygraph Graph Options Screen 14 6 THE GRAPH OPTIONS MENU The Graph Options
174. screen and menu shown in Figure 14 5 provides control over the graph background parameters These include parameters which allow control of the axis style the graph limits titles and axis labels and the numeric tickmark labeling and spacing The menu line appears as follows Axis Parameters Tick Parameters Graph Limits Title Labels Reset Quit Axis Parameters The Axis Parameters option allows the selection of the type of axis style for the plot The screen field accessed from this option is a toggle field The choices available are Half left and bottom axes only Full left right top and bottom axes and Grid the same as Full but major tick marks are extended across to the opposite axis The default is Full Tick Parameters The Tick Parameters option allows specification of the nature of the numeric tickmark labels to be placed along each axis This is accomplished with a set of closely inter related parameters which control the format of the labels The default values are initially set to Auto and provide adequate labels for most data With the appropriate selection of parameter values however many useful labels may be constructed including fractions and superscripted powers of ten An excerpt from the NCAR documentation on tick parameters is included in the appendices Certain incompatible combinations of parameter choices will result in no labels being plotted or error messages generated by the NCAR Autograph utili
175. se the Krige Options screen and menu to be displayed and a message will be generated to indicate that the results were successfully written to the output file If an error occurs while attempting to write to the file kriging will be halted and an error message will be displayed How to Cancel Kriging At any time during the kriging process kriging may becanceled by pressing the lt ctrl gt and lt alt gt keys the lt ctrl gt and lt shift gt keys or the lt left shft gt and lt right shft gt keys simultaneously and holding them down until the next point or block has been kriged If this is done a message 8 displayed indicating that kriging has been terminated This is useful when the debug screers reveal a problem with the search or variogram parameters and you wish to change them and re start Note that in this situation the output file will not contain a completed grid of estimates and probably cannot be used by the program Conrec It is important to remember that the terminate kriging keys will not work when any of the three debug display keys is active 12 6 THE VARIABLES MODELS MENU Variables and Models Selection List of Variables Variable Cadmium Global Mean to Krige Cadmium J Variogram Model Parameters Nugget 4 500 Sill Value Major Range Minor Range Angle 1 2 3 4 5 6 7 8 9 0 1 Edit Delete Quit Add a new variable and model to the Kriging List i uI Figure 12 4 Krige Variables Models Screen
176. sed from this option are X Variable A toggle field for selecting the variablename whose values will be used as the X coordinates The default X variable is the first variable in the data file Y Variable A toggle field for selecting the variable name whose values will be used as the Y coordinates The default Y variable is the second variable in the data file Contour Variable A toggle field for selecting the variable name whose values will be used as the contour values The default Contour Variable is the third variable in the data file Graph Options The Graph Options option provides access to the Graph Options screen and menu described below Contour Options The Contour Options option provides access to the Contour Options screen and menu described below Execute When the Execute option is selected you will be prompted for a metacode file name The metacode file is then created and the graph is displayed The metacode file name may be up to 14 characters The default name is METACODE MET If thedefault value is not used and the file already exists a Yes No prompt provides an option to proceed or quit The metacode file is stored on disk for later use A hard copy of the graph can be obtained by using the progran Hpplot and an HPGL compatible plotter If the number of contour levels is set to zero an error message is displayed The user must set the number of contour levels before the graph can be produced Contour lines will
177. ssed This option R discussed in detail in the section below Common Menu Options Although the programs place no restriction on file extensions it is good practice to use consistert naming conventions for file extensions Below are the suggested extensions which are used as defaults in Geo EAS programs Geo EAS File Extensions TXT an ASCII text file DAT a Geo EAS data file PCF a pair comparison file created by PREVAR read by VARIO GRD a gridded Geo EAS data file could be produced by KRIGE CPF CONREC parameter file KPF KRIGE parameter file XPF XYGRAPH parameter file POL Polygon boundary file used by KRIGE MET metacode graph file created by CONREC POSTPLOT and XY GRAPH and used by HPPLOT and VIEW PLT plotter instruction file produced by HPPLOT 3 1 3 System Defaults Option This option allows you to disable the introductory screens which appear when programs are initiated The System Defaults File GEOEAS DEF contains defaults for the programs to use at start up The first record contains the most recently used File Prefix The second contains the most recently used data DAT file name These records ate automatically updated when a program is terminated so that this information may be passed to the next program used If the file does not exist when a program is started it will be created when a program is finished A third record has been added to GEOEAS DEF to allow you to disable the i
178. statistics it canbe seen that this data set is nearly symmetrical about the mean value the mean is close to the median and approximately halfway between the minimum and maximum values There are no suspect outliers The probability plot shows that the data set approximates a normal distribution a probability plot is a cumulative frequency plot scaled so that a normal distribution plots as a straight line Whether a distribution is normal log normal or something else has no particular geostatistical significance except that it is often more difficult to interpret variograms for highly skewed distributions such as the log normal and in such cases it may be useful to also compute variograms on log transformed data 4 3 VARIOGRAM ANALYSIS The computation interpretation and modeling of variograms is the heart of a geostatistical study The variogram model is your interpretation of the spatial correlation structure of the sample data set It controls the way that kriging weights are assigned to samples during interpolation and consequently controls the quality of the results All interpolation and contouring methods make the assumption that some type of spatial correlation is present that is they assume that a measurement at any point represents nearby locations better than locations farther away Variogram analysis attempts to quantify ths relationship How well can a measurement be expected to represent another location a specific distance
179. sulting univariate statistics are Weighted the statistics are calculated for Weight value multiplied by Y arab value The default weighting factor vanable is None in which case the weighting factor is 1 Log Option A two valued toggle On Off field to enable or disable the Log option If the Log option is enabled and a weighting factor variable selected then the statistics are calculated for the Weight value multiplied by the natural log of the Variable value Whenever the Log option is enabled sample values less than or equal to zero are counted but not used in the computation The default value is Off Limits The Limits option allows computation of statistics for a subset of the data which lie between the specified minimum and maximum sample values You may specify the upper and lower limits placed on the values used for computing the basic statistics Minimum A numeric field which contains the lower limit on the sample values used in the computation The default value is the minimum value of the selected variable Maximum A numeric field which contains the upper limit on the sample values used in the computation The default value is the maximum value of the selected variable Execute The Execute option provides access to the Results screen and menu When the Log option R enabled the number of samples less than or equal to zero is displayed F this occurs pressing any key provides access to the Results screen See the sect
180. ted by the omnidirectional model Obviously one cannot be too precise about fitting ranges to these directional variograms Likewise it would not be worthwhile to attempta more precise definition of the direction of maximum and minimum range The program Krige assumes that the directional variogram model ranges form an ellipticd pattern It is therefore only necessary to fit models to the major and minor axis directions define the entire 2 D structure One could make a case for the rangeof the major axis 0 degrees of the exponential model being anywhere between 250 and 400 units and the minor axis 9 degrees being between 60 and 120 units We will settle on a model with major and minor axes of 300 and 100 units respectively and move on to kriging A note on alternate types of variograms The Type option on the Variogram Results screen allows you to select and plot any of three alternate estimators of spatial variability These ae sometimes less sensitive to outliers skewed distributions or clustered data than ordinary variograms and may help you recognize a structure when the ordinary variogram is too noisy The relative variogram is analogous to the relative standard deviation often used to measur analytical variability The madogram plots the mean absolute differences They are not true variograms because they are not based upon squared differences The Inv Cov variogram is a relatively new method Srivastiva 1988 based on estimat
181. tes that no symbols are to be plotted The default Symbol Types for the six variables are 1 through 6 Line Type Six toggle fields for selecting the type of line to plot for each variable There are six choices available 0 through 6 A value of 0 indicates that no line is to be plotted The default Line Type for all six variables is 0 Color Six toggle fields for selecting the color to plot the symbol and or line pattern The choices available are Black Blue Red Yellow Green Brown The default color is unique for each variable Regression The Regression option provides access to a two valued Yes No toggle field to enable or disable the calculation of linear regression If the value is Yes linear regression is only calculated for the first Y variable The regression line and the regression coefficients are plotted on the graph The coefficients are the slope and intercept of the line represented by the equation Y Slope X Intercept The R Squared value a measure of correlation is also plotted The default is No Legend The Legend option provides access to a toggle field that is used for selecting the position of the graph legend The choices available are None no graph legend Bottom at the bottom of the graph and Right at the upper right hand corner of the graph The default position is None no legend Graph Options The Graph Options option provides access to the Graph Options
182. the X and Y coordinate values Max Two numeric fields for entering the maximum coordinate value to be used on the X and Y axes The default values displayed are determined from the variables selected as the X and Y coordinate values Titles Labels The Titles Labels option allows you to enter the title and labels for the graph The Hershy character sets of 33 fonts are used for plotting alphanumeric labels Also certain special characters may te embedded in the title or label which control selection of alternate fonts or other aspects ofthe plotted text These special characters are not plotted but are interpreted as commands by the metacock translator software The appendices contain information on font selection codes The screen field accessed from this menu option are Main title An alphanumeric field which may contain up to 60 characters for the main title of the graph The default title contains the variable name selected as the pot variable and the name of the data file Subtitles Two alphanumeric fields which may contain up to 60 characters each for the subtitles on the graph The subtitles appear below the main title X Label An alphanumeric field which may contain up to 60 characters for the X axis label The default label is composed of the X variable name followed by its units in parentheses Y Label An alphanumeric field which may contain up to 60 characters for the label on the Y axis The default label is composed of
183. the univariate statistics for cadmium Figures 4 5 and 4 6 display the histogram and probability plot for cadmium RESULTS Data File C GeoEASSNDataSExamp le dat Variable gt Cadmiun Lower Limit Upper Limit Observations Missing Data Retained S Sum of Weights 60 0000 Mean S 7 8850 Minimum Value S 0000 Variance 15 5315 25th Percentile 5 3000 Std Deviation 3 9410 Median i 7 9500 Coef Variation 49 9809 75th Percentile 10 8000 Maximum Ua lue i 16 7000 Skewness E 1510 Kurtosis 2 4639 Probability Plot Examine Quit Choose histogram parameters display graph Figure 4 4 Statl Results Screen Histogram Data file Example dat Statistics N Total N Miss N Used Mean Variance Std Dev S Cy 2 Skewness Kurtosis Minimum 25th x Median YSth x E i Maximum 2 16 Cadmium ppm Frequency 8 1 Figure 4 5 Histogram of Cadmium Normal Probability Plot for Cadmium 64 B 64 885 531 941 981 151 464 6648 5388 958 868 TBB Data file Example dat Statistics N Total N Miss N Used Mean z C U E S E z M Minimum 25th Median 75th Z Maximum Cumulative Percent Figure 4 6 Cadmium Probability Plot Variance Std Dev Skewuness Kurtosis 64 B 64 885 531 941 981 151 464 468 S48 958 868 From the histogram and the
184. the Color Graphics Adapter CGA and the Enhanced Graphics Adapter EGA At least 512 kilobytes Kb of random access memory RAM is required but 640 Kb is recommended An arithmetic co processor chip is strongly recommended due to the computationally intensive nature of the programs but is not required for use Programs may be run from floppy diskette however a fixed disk is required to use the programs from the system menu The system storage requirement is approximately three megabytes For hardcopy of results a graphics printer IBM graphics compatible is required Support is provided for plotters which accept HPGL plotting commands Geo EAS DISTRIBUTION Geo EAS softwareand documentation are entirely in the public domain and may be copied and distributed freely Geo EAS 1 2 1 1 1 Introduction 1 4 USER PROFILE To use this system you should have some familiarity with personal computers and DOS Disk Operating System You should understand basic DOS commands such as DIR Directory CD Change Directory and how to insert and use diskettes For more information on these topics consult a DOS user s manual It is assumed that you have a working knowledge of Geostatistics and that you understand the basic Geostatistical concepts For a list of references on the subject of geostatistics refer to Appendix A References Geo EAS 1 2 1 1 2 March 1991 SECTION2 SYSTEM SUMMARY 2 1 INSTALLING THE SYSTEM 2 1 1 The Distribution D
185. the Number of Sectors parameter If one sector is chosen then this field is disabled If more than the specified number of consecutive sectors are empty no value is kriged missing values are generated in place of an estimate and kriging standard deviation Model The Model option allows specification of the variogram model to use when kriging Screen fields are provided for a nugget effect value and up to four nested variogram structures Each structure is specified with a structure type a sill value and an ellipse of influence If simple kriging R chosen an additional field is provided for entering the Global Mean Each of the four structures has five associated screen fields Selecting the Model option will cause a cursor bar to appear in the upper left corner of the models area The arrow keys may be used to move the cursor bar to fields in the Model area To exit the Model area move the cursor bar out of the top or off to the left of the area using lt left gt or lt up gt If any errors are made when entering variogram model parameters an error message will be displayed and the cursor bar will be placed at the problem field The major and minor ranges and the angles for the additive variogram structures defined in this parameter group are similar to the search ellipse ranges and angles Figure 11 3 illustrates how these parameters define the shape of the ellipse The screen fields accessed from this option are Nugget a numeric field fo
186. the Y variable namefollowed by its units in parentheses Reset The Reset option allows the user to reset the graph options parameters to their default values SECTION 14 XYGRAPH 14 1 WHAT XYGRAPH DOES Xygraph produces line and or scatter plots for up to six variables in a Geo EAS data file Plots of up to six dependent variables with one independent variable can be obtained Up to sx colors symbols and line types may be used to identify the data Options allow a regression line to be calculated and axes parameters and graph labeling to be controlled A file called a metacode file is created for redisplay or to produce a hardcopy 14 2 DATA LIMITS Xygraph requires that the input data file contain at least two but not more than 48 variables The data file may contain up to 500 samples If the data file contains more than 500 samples only 500 will be used by Xygraph 14 3 THE MENU HIERARCHY Xygraph _ _ Prefix Read Parameters Options Execute ___ Data Variables Symbol Line Regression Legend Graph Options___ Axis Parameters Tick Parameters Graph Limits Titles Labels Reset Quit Execute Quit Save Parameters Quit 14 4 THE MAIN MENU The Main screen and menu Figure 14 1 has the options to allow specification of the input and output parameter file names The menu line appears as follows Prefix Read Parameters Options Execute Save Parameters Quit xYGRAPH 1 2 1 fm X Y graph plotting program Fi
187. the programs Read Parameters Save Parameters These options are common to all Geo EAS programs which make use of Parameter Files Parameter Files are files which contain values for all parameter choices available in a particular program Ifa program provides this feature you may save the values of parameters for later use by using the Save Parameters option Selection of this option will result in a prompt for the output parameter file name The File Prefix is used to create or access the file The Read Parameters option is used to load the parameter values into the program When this option is selected an input parameter file name must be entered Typically a program will attempt to load all data and set all parameter values based upon the information in the input parameter file It is assumed that the data file associated with the parameter file is in the same location subdirectory etc as it was when the parameter file was saved If any erros occur while accessing or reading the parameter file or the associated data file an error message will be issued and the program will re initialize all parameter values to their defaults Conventions should be used when naming parameter files so that they can be associated with the appropriate data files and programs A suggested convention for file extensions is given in a previous section File Naming Conventions It is also suggested that the first part of the file name have some similarity to the asso
188. to the output file when the Execute option is selected The variables are selected from a toggle field After each selection the variable name is displayed on the screen and a yes m prompt appears asking if you want to select another variable If yes is indicated then you are prompted for another variable If no is indicated then control is returned to the Column Extract menu Execute Upon selection of this option the selected variables andrelated data are copied and stored in the output file When the operation is complete a message is displayed Upon pressing any key control is returned to the Column Extract menu Row Extract Upon selection of this option the Row Extract menu is displayed The Row Extract mem provides the options necessary to perform row extraction This operation extracts samples from the specified input Geo EAS data file based upon a test condition The menu line appears follows Files Subsetting Condition Execute Quit Files This option is used to specify two files The name of first file entered an input file is a Geo EAS data file The name of the second file entered is an output file Subsetting Condition This option is used to specify a test condition The test condition is of the form lt Operand1 gt lt Relation gt lt Operand2 gt where lt Operand1 gt is a variableand lt Operand2 gt can be a variable or a constant lt Relation gt can be LT LE Less than Less than or equal to GT
189. ts in the specified output Geo EAS data file An example is shown in the Execute option The menu line appears as follows Files Execute Quit Files This option is used to specify two data file names The first an input file is a Geo EAS data file The second is an output file After the two files have been specified the variable names stored in the input file are displayed Execute Upon selection of this option the data from the input file are stored in a temporary file Duplicate records are deleted and the data are storedin the specified output file When the entire process is complete a message stating that the data have been sent to the output file is displayed Upon pressing any key control is returned to the Compress menu As an example of the Compress operation the following output file Out5 dat was generated when the input file Demol dat was compressed Out5 dat follows Out5 dat Demol dat ficticious data set 1 3 Easting feet Northing feet Arsenic ppm 320 0 311 0 850 119 0 119 0 630 115 0 111 0 560 114 0 269 0 1 02 431 0 137 0 670 N ote that all duplicate records have been deleted ID Variable Upon selection of this option the ID Variable menu is displayed The ID Variable menu provides the options to create the variable Sequence The Sequence denotes the sequential position of the data in the input file An example of this is shown in the Execute option The menu line appears as follows
190. ty These errors will cause the program to terminate To recover restart and change the parameters A menu option is provided to reset these parameters to Auto so that the default values may be used Refer to Section 5 9 Postplot for several examples of numeric tickmark labels The Screen fields accessed from this option are Base Two numeric fields for the computation of major tick marks along the X and Y axes The user may accept the default value of Auto which allows the system to select the appropriate value or enter a value appropriate for the variable selected Type Two toggle fields for selecting a formula for computing using Base entered above the spacing of the tick marks along the X and Y axes The available choices are Auto System will select appropriate computation None No tick marks on axis Base k Base 104k Base k Note k is an arbitrary integer computed by the program The default value is Auto for both axes Label Two toggle fields for selecting the format of numeric label to be used at the major tick marks along the X and Y axes The available choices are Auto System will select appropriate format None No tick marks on axis Scien Scientific notation Expon Exponential notation No Exp Non exponential notation Fraction Two numeric fields for entering the number of significant digits to display in the numeric labels along the X and Y axes Exponent Two numeric fields for entering
191. uate for most purposes If an invalid or unsuitable format specifier is entered an error message is displayed For more information on FORTRAN format specifiers refer toa FORTRAN reference manual Tickmark Label Size A toggle field used for selecting the character size of Titles Labels the tickmark labels The choices available are 1 to 10 The default size is 3 This value works well on the screen however a smaller size might be more suitable for output to a plotter The Titles Labels option allows you to enter the title and labels for the graph The Hershey character sets of 33 fonts are used for plotting alphanumeric labels Also certain specid characters may be embedded in the title or label which control selection of alternate fonts a other aspects of the plotted text These special characters are not plotted but are interpreted as commands by the metacode translator software The file HERSHY BAR included with the software contains the font information See the appendices for more information on fort selection codes The screen fields accessed from this menu option are Title Position Two toggle fields for selecting the position of the main title and the Main Title Subtitles X Axis Y Axis Size subtitles The choices available are Left at the left edge Center centered on the line or Right at the right edge The default is Center An alphanumeric field which may contain up to 60 characters
192. ults screen and menu provides options to display a probability plot described below to display a ranked listing of data values and order statistics shown below as Examine Data and to display the Histogram screen and menu The Results Screen displays univariate statistics for the selected variable The menu line appears as follows Histogram Probability Plot Examine Quit Histogram The Histogram option provides access to the Histogram screen and menu First a defaut histogram is displayed See the section on the Histogram menu below for more information Probability Plot When the Probability Plot option is selected a probability plot Figure 7 3 is computed and displayed on the screen The plot is a graph of the ranked variable values plotted against their cumulative percentiles The vertical axis is scaled in units of the variable and the horizontal axis is scaled in units of cumulative percent A boxplot appears at the right side of the plot area along with univariate statistics the quartiles and the minimum and maximum values Figure 7 3 Statl Probability Plot Normal Probability Plot for Cadmium 2 Data file Example dat Statistics N Total 68 N Miss 4 N Used 68 Mean 885 Variance 531 Std Dev 941 AU l 981 Skewness 151 Kurtosis 464 E L m E T m M Minimum BHA 25th 2 368 Median 956 75th 2 868 Maximum TOB Cumulative Percent Figure 7 3 Stat 1
193. va R M 1989 An Introduction to Applied Geostatistics Oxford University Press Inc New York Journel A H and C H Huijbregts 1978 Mining Geostatistics Academic Press London Rendu J M 1981 An Introduction to Geostatistical Methods of Mineral Evaluation South African Institute of Mining and Matalurgy Johannesburg Srivastava R M 1988 A Non ergodic Framework for Variograms and Covariance Functions SIMS Technical Report No 114 Dept of Applied Earth Sciences Stanford University APPENDIX B NCAR GRAPH OPTIONS The following is an excerpt from the NCAR Autograph Manual It has been slightly modified to include the Tickmark parameter names used in programs Xygraph and Postplot This explanation may help to explain how these parameters work together to produce numeric tickmark labels Acceptable actual values for the screen fields are as follows No Labeling Setting label to None turns off the numeric labels on the axis specified The other parameters are then ignored Scientific Labeling Setting Label to Scien selects scientific notation Each numeric label is written in the form i L f 10 e Where brackets enclose portions which may be independently present or absent and e is a superscricpt exponent The value of the parameter Type is immaterial when scientific notation is selected The parameter Exponent specifies the number of character of I thus also specifying the value o
194. value is Yes the default four different symbols in four different colors will be plotted to represent the values within their quartiles A legend is also plotted to show the quartile cutoff values the symbols and their corresponding colors If the value is 1 only one symbol a in one color yellow will be used to plot the values No legend will be plotted Graph Options The Graph Options option provides access to the Graph Options screen and menu described below Execute When the Execute option is selected you will be prompted for a metacode file name The metacode file is then created and the graph is displayed The metacode file name entered may be up to 14 characters The default value is Metacode met If the default value is not used and the file specified already exists a Yes No prompt for whether or not to overwrite the file is displayed This file contains the metacode instructions produced by the program It will be saved for future viewing A hard copy of the graph can be obtained by using the program Hpplot and an HPGL compatible plotter After the graph has bem displayed type lt q gt to clear the screen and return to the Main menu An example post plot is shown in Figure 13 2 Pestplot cf Cadmium from data fila exameple dat 409 Esating Teat Tet Guortile 000 oOo 2nd Suartils 3 300 7 600 Ord G uortile 7 600 10 8606 4th Guortile 10 500 16 700 Figure 13 2 Example Post Plot 13 5 THE GRAPH OPTIONS MENU
195. will be performed If Simple kriging is chosen simple kriging is performed and a value must be entered for the Global Mean when the Model option is selected Search The Search option provides a means of controlling the neighborhood search used during kriging Parameters may be specified to define an elliptical search area Constraints may be placed upon the number of sectors and the number of samples to be retained in each sector of the search area and the type of distance measure to use when eliminating neighbors from a search sector Figure 11 3 depicts the search parameters which define the shape of the search ellipse EE ____________ ________ Search Ellipse and Variogram Anistropy Ellipse Parameters R Minor X Coordinate Axis Figure 11 3 Search and Variogram Ellipse Parameters The screen fields accessed from this option are R Major R Minor Angle Min Dist Distance Type a numeric field for indicating the length of the major radius half the length of the longest axis of the search ellipse a numeric field for indicating the length of the minor shortest radius of the search ellipse This value must be less than or equal to R Major non zero and non negative The default value is the value given for R Major If R Major is equal to R Minor the search area will be a circle a numeric field for indicating the orientation of the search ellipse It is given in trigonometric degrees in the range from
196. wo sample coordinate variables and the sample value variable chosen for kriging The remaining four variables are named Zstar Zsdev Zstar Z and Zscore They contain respectively the estimate the kriging standard deviation the estimation error and the zscore estimation erra divided by the kriging standard deviation This file may be used with other Geo EAS programs for further analysis Examine The Examine option provides a means of directly examining individual results ofkriging on a scrolling display called the Examine Results screen This screen is shown in Figure 11 9 The observed values estimates errors kriging standard deviations and zscores are displayed n columns on this screen These values are ranked in order of estimation error so that the largest negative difference is at the top of the list and the largest positive difference is at the bottom of the list The leftmost column contains the sample sequence number in the input data file The lt up gt lt down gt lt pgup gt lt pgdn gt lt home gt and lt end gt keys may be used to position the list on the screen The numeric keys lt 1 gt through lt 9 gt are used to scroll the list in increments of 10 e g pressing lt 5 gt would position the middle of the list on the screen The lt q gt key is used to exit the Examine Results screen and return to the Results screen and menu EXAMINE RESULTS Observation Est imate Difference kriging 900 8 18
197. xes parameters and titles A file called a metacode file is created for redisplay or to produce a hardcopy Note Postplot attempts to produce true scale graphs on the screen but for some data configurations an internal NCAR routine overrides true scaling and produces a somewhat distorted graph 13 2 DATA LIMITS Postplot requires that the input data file contain at least 3 but not more than 48 variables These should consist of an X and Y coordinate and a third variable which will be posted The data file may contain up to 1000 samples If the data file contains more than 1000 samples only 1000 will be used by Postplot 13 3 THE MENU HIERARCHY Postplot__ Prefix Data Variables Options Graph Options __ Axis Parameters Tick Parameters Graph Limits Titles Labels Reset Quit Execute Quit 13 4 THE MAIN MENU The Main screen and menu shown in Figure 13 1 has the options to allow specification of the data and metacode file names the selection of the variables to be used and the options for displaying the posted variable The menu line appears as follows Prefix Data Variables Options Graph Options Execute Quit POSTPLOT 1 2 1 A program for plotting 2D sample locations and values File Prefix C GeoEASNData Variables X coordinate variable Easting Y coordinate variable Northing Execute Variable to post Cadmium Use this option to create the Opt ions plot The plot will be saved in Include Values No
198. y as the search ellipse with two ranges radii and an angle Note however that the two ellipses have fundamentally different purposes although the parameters which describe them are the same A numeric field for indicating the length of the minor shorter range of the variogram ellipse This value must be non zero non negative and less than or equal to the Major Range The default value is the Major Range value If the two ranges are equal an isotropic variogram structure is defined If they are not equal the two ranges are used to determine the ratio of anisotropy A numeric field for indicating the orientation of the ellipse for the variogram structure It is given in trigonometric degrees in the range from zero up to but not including 180 and indicates the angle between the longest axis of the ellipse specified by the Major Range and the sample coordinate X axis If the two ranges are equal isotropic structure then the angle is ignored The Delete option is used to delete a variable and model from the kriging list When this option is selected the Kriging List menu will be activated and the variable to delete may be selected as described in the Edit option Once this selection is made a Yes No prompt provides the alternative of canceling the deletion If lt y gt is chosen the vanable and model will be deleted and the Kriging List and screen will be regenerated This option is disabled when the Kriging List is empty Plot of
199. y erroneous keystrokes such as alphabetic keys with a low pitched error tone An example of numeric fields in program Stat are the two fields accessed through the Limits option Only numeric values may be entered into these fields Values must be entered in the conventional manner legal characters are lt 0 gt through lt 9 gt and lt gt exponential notation for numeric values is not allowed Toggle Fields A toggle field is a special type of field which contains a list of 2 or more preset choices Only one of these choices is displayed in the field The lt space gt key is used to change the displayad choice and the lt enter gt key is used to make the selection Two examples of toggle fields in program Stat are the Variable field and the Log field Once a file name has been specified the Variable toggle field will contain the names of all variables in the file When the Variable option on the menu line is selected this field will be highlighted and each time the lt space gt key is pressed a new variable name will appear in the field When the desired variable name appears press the lt enter gt key to select it The Log field is an example of a toggle field with only two choices On or Off If On is chosen then statistics will be calculated for the log of the selected variable Yes No prompts prompts for additional information These prompts are for information which will not be displayed permanently on the scr
200. yed and a message indicating that the data have been sent to the output file appears Pressing any key returns control to the Merge menu To describe the merge process assume that File1 is the first file name entered and File2is the second file name entered If one input file is smaller than the other input file then the smaller file has missing values added to its variables Variables that appear in both input File and input File2 are combined with the samples of File preceding those of File2 The specified output file stores the results of the merged files An example best demonstrates the merge operation The output file Out3 dat which follows displays the merging of input files Demol dat as Filel and Demo2 dat as File2 Out3 dat Demol dat ficticious data set 1 4 Easting feet Northing feet Arsenic ppm Lead ppm 320 0 311 0 850 300 119 0 119 0 630 360 115 0 111 0 560 700 114 0 269 0 1 02 500 114 0 269 0 1 020 710 431 0 137 00 6700 1 E31 k NOTE The variables appearing in both input files are combined into one variable Easting and Northing and these variables took on the values from the first file Report Upon selection of this option the Report menu is displayed The Report menu provides the options necessary to generate a listing of specified variables in Report form The Report listing is described in the Execute option The menu line appears as follows Files Variables Execute Quit Files This option i
201. zero up to but not including 180 and indicates the angle between the longest axis of the ellipse specified by R Major and the sample coordinate X axis If R Minor is equal to R Major a circle search is used and the Angle parameter is ignored a numeric field for specifying the minimum distance from the estimated sample location to the nearest neighbor sample Ifa minimum distance of zero the default is specified then any neighboring sample will be used subject to the complete set of search constraints a two valued toggle field for selecting the type of distance measure to use when eliminating neighbors The choices available are Num Sectors Max Pts Sector Min Pts to Use Empty Sectors Euclidean the default and Variogram Neighboring samples are eliminated from consideration when the Max Pts Sector Maximum points per sector criterion is exceeded in a given sector If this should occur only the closest neighbors are kept If Euclidean distance type is chosen neighbors are eliminated based upon the euclidean distance from the point to be estimated ellipse center If Variogram distance is chosen the variogram function value as specified by the Model parameters for the computed distance is used as the criterion for elimination of neighbors a toggle field for selecting how many sectors in which to divide the search ellipse The choices available are 1 the default 4 and 8 The combination of the

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