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1. Variograms Window siessen aana o E aE E Semivariance Values Window sse Isotropic Variogram Models sese The Spherical Isotropic The Exponential Isotropic The Linear Isotropic The Gaussian Isotropic Anisotropic Variogram Models The Spherical Anisotropic The Exponential Anisotropic The Linear Anisotropic The Gaussian Anisotropic Anisotropic Semivariance Surface 2 Variogram Map Cross Autocorrelation or Cross Semivariance Analysis Chapter 7 Other Autocorrelation Measures Standardized Variograms ssssssssssseeeeen nens Madogtams tee ue ae et dete Oe ree eee ta we da Table of Contents Fodogralms tote reiten 97 ER 98 Gorrelograms et eei emen 99 Covariance Analysis sse 100 General Relative
2. this statistic provides a measure of the proportion of sample variance Co C that is explained by spatially structured variance C This value will be 1 0 for a variogram with no nugget variance where the curve passes through the origin conversely it will be O where there is no spatially dependent variation at the range specified i e where there is a pure nugget ef fect Statistics AutoFit Statistics for the Autofit model the model most recently calculated by GS appear in this box In this way you can compare your changes to model terms against that calculated automatically Autofit Automatically refit the model using as starting conditions the parameters in this dia log window Model fitting in GS is somewhat dependent on starting conditions as sumed model parameters prior to iterations Sometimes you can fit a better model by hand in which case Refitting will further refine parameters to minimize RSS To return to the original model parameters you may need to exit this Model definition window and recalculate the variogram OK Cancel Press OK to close the dialog window and apply any changes made to individual models Press Cancel to exit the dialog window without applying changes Chapter 6 Semivariance Analysis Overview Spherical Isotropic Model The spherical isotropic model is a modified quadratic function for which at some dis tance Apo pairs of points will no longer be autocorrelated and the s
3. 101 Pairwise Relative Variograms 103 Morans T Analysis 25 ERE eoa 104 Fractal Analysis ciet tete 106 Chapter 8 Variance Clouds and h Scattergrams OVEIVIGW tei iae tete nce ita MU eei E ds 107 Variance Clouds sssssssssssssseenenneeeen nennen 107 Variance Cloud Pairs ssssssssssseeee eene 111 h Scattergrams sei dab nap cente ete dudum 112 h Scattergram Pairs sse 115 Chapter 9 Interpolation Basics OVEIVIEW icra Ere ce bte ot eit a 116 The Interpolation Window snm 117 Z Estimate Boundaries sssssseeeeneenne 121 Defining a Regular Interpolation Grid 121 Defining an Irregular Interpolation 123 Polygon Outlines Interpolation Masks 125 Polygon Outline Map sese 127 Cross Validation and Jackknife Analysis 128 Cross Validation and Jackknife Values 130 Chapter 10 Conditional Simulation OVGIVIOW MI NELLE reiecit ium era 131 Secondary Data for 133 Number of Simulations sssssssseeeenneene 134 Chapter 11 Kriging and Cokriging eU ITI 13
4. be grouped in one of three distributions Quantiles in which Z data are placed into groups of equal frequency i e into groups that have the same number of sample values Quartile distributions are divided into 4 groups percentiles into 100 groups etc Intervals in which Z data are placed into groups based on even intervals of the data range without regard to how many sample values are placed in each group Custom in which you can define how groups are formed Note that this coordinate posting is different from the posting available from the Map Window The Map Window posting uses data saved with the interpolation file this posting uses nonmissing data in the current Data Worksheet 63 Chapter 5 Summary Statistics Levels Set the Number of levels corresponding to different symbols to any value be tween 1 and 10 For values of 1 the legend will be suppressed Set the Type of level to correspond to how symbols are assigned to locations Quantiles divide the domain into an equal number of sorted values per level In the example above quartiles there are as many values greater than the median of 0 34 as there are less than 0 34 Choose Intervals to divide the range into even intervals e g in the example above in which values range from 0 to 1 25 choosing Intervals would divide the data range of 0 1 25 into 4 levels 0 3125 0 625 0 9375 and 1 25 Define provides the opportunity to define cust
5. Kriging Type Ordinary External Drift Define PolynomialTrend Define Simple e Stationary Nonstationar y IV Indicator Cutoff 84 4 r Variogram Isotropic C Anisotropic Use Relative Discretization C Point Kriging Block Kriging x 224 v 22 Kriging Type GS provides both ordinary and simple kriging Ordinary kriging the most common ly used type of kriging assumes a constant but unknown mean that may fluctuate among local neighborhoods within a study area In ordinary kriging the sum of kriging weights equals to one Ordinary kriging can be performed with external drift or with a polynomial trend Kriging with a trend also called universal kriging employs a prior trend model which is defined as a smoothly varying deterministic function Five different polyno mial trend terms can be included in the model X linear Y linear X quadratic Y quadratic and XY quadratic use the Define command to specify which terms to in clude 135 Chapter 11 Kriging and Cokriging 3 v XLinear X Quadratic M YLinea M Y Quadratic Cancel Kriging with an external drift is an extension of kriging with trend The trend model is limited to two terms m u a0 a f u where m is the mean value for estimation neighborhood u and f u is set to the secondary external drift variable Use the Define command to assign a drift term to every interpolation grid point
6. north X Coord Y Coord east 0 00 0 00 0 00 100 0 00 200 86 1 Cancel 0 00 3 00 90 0 0 00 4 00 147 8 0 00 5 00 329 7 0 00 6 00 127 5 8 0 00 7 00 132 0 0 00 800 499 4 0 00 9 00 797 0 00 10 00 351 0 12 1100 304 8 0 00 12 00 m Clear Clear existing data from worksheet Fill X Y Fill the X and Y Coordinate columns with calculated values based on the regular interpolation grid defined in the Interpolation window If a regular grid is not defined in the interpolation window this button is not available Import Import values from an external text file Each record of the file must contain a sepa rate x y and secondary data value separated by commas tabs or spaces See Chapter 4 Importing Data from External Files for instructions on importing Other Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or the right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or the Data Change Decimals menu command Click on the top of a column to Sort the worksheet based on the column selected in alternat ing ascending or descending order You may also change Column Widths by plac ing the cursor over the line between two columns and dragging to a new location 133 Chapter 10 Conditional Simulation Number of
7. or expensive to measure and it is correlated with a more available covariate cokriging can greatly improve interpolation estimates See Cokriging Analysis for further information Commas as Column Title Separators Column or variate names are separated by commas e g m east m north Pb ug g pH Comma Separated Values Values within data records separated by commas 13 2 34 5 35 6 0 15 Conditional Simulation An advanced interpolation technique whereby Z estimates are based on a form of stochastic simulation in which measured data values are honored at their locations Covariate The Covariate is a second Z variate that covaries with the primary Z variate It is used in cokriging Data Builds Data in the GS Worksheet is read into the actual arrays that get analyzed during Data Builds Data builds occur whenever a new data set is read into GS via the Import command or whenever a field assignment or data value is changed and the Rebuild Button Data Worksheet Window is pressed During data builds missing values are ignored and filters and transformations are applied Most Data Builds are automatic you ll need to force a Data Build whenever the Rebuild Button is red the Data Summary Window will also be empty Data Fields A data field is an individual item on the data record In the GS Worksheet records appear as rows and fields appear as columns Prior to analysis you must identify an X coordinate field a Y coordinate
8. This value overrides the missing value in dicator specified in the Preferences General dialog or the map input file Intervals e read contour intervals from a text file the first value of each record of line of the file is presumed to be a separate interval The default file exten sion for Interval files is Ivl e Save save the existing contour intervals to a text file e Reset recalculate intervals based on a regular distribution even intervals between the lowest and highest value in the file Color Source e Standard specifies a default color pattern of red orange yellow violet e Blue specifies a default color pattern of different shades of blue e Custom specifies a custom color pattern defined below e Red specifies a default color pattern of different shades of red e Green specifies a default color pattern of different shades of green e Gray specifies a default color pattern of different shades of gray Color Source Custom e Get get a custom color pattern saved earlier The initial custom color is the same as the standard color source above e Save save the existing color pattern as the custom color pattern e Reset reset the custom color pattern to the default Standard pattern Color Source Dynamic Expands or contracts the color range when there are fewer than 15 intervals speci fied For example if 10 intervals are specified and the Dynamic box is not checked the
9. 83 Chapter 6 Semivariance Analysis Overview Linear Isotropic Model The linear isotropic model describes a straight line variogram Note that there is no sill in this model the range Ao is defined arbitrarily as noted below The formula used is y h Co C Ao where y h semivariance for interval distance class h h lag interval Co nugget variance gt 0 C structural variance gt Co and A range parameter In the case of the linear model there is no effective range A spatial auto correlation occurs across the entire range sampled in GS model windows A is set initially to the separation distance for the last lag class graphed in the variogram below this would be 77 4 Variogram Linear Model 0 254 0 191 Semivariance eo 2 m 8 0 0 20 5 41 0 61 5 821 Separation Distance h 84 Chapter 6 Semivariance Analysis Overview Gaussian Isotropic Model The Gaussian or hyperbolic isotropic model is similar to the exponential model but assumes a gradual rise for the y intercept The formula used for this model is y h Co C 1 exp Ao where y h semivariance for interval distance class h h lag interval Co nugget variance gt 0 C structural variance gt Co and Ao range parameter In the case of the Gaussian model the effective range A 39 which is the distance at which the sill C Co is within 596 of the asymptote
10. Data Summary Window Regression Analysis Tab The Data Summary Window Regression Tab is available when a covariate is as signed in the Data Worksheet Window via the Field Assignment Dialog Information for the Z variate or Covariate is provided in a separate Z Variate tab and for the co ordinate variates in a separate X Y Coordinates tab as described earlier The scat ter plot is a plot of the cross variate regression see below Data Summary Covariate X Y Coordinates Covariate Z2 d Regression Statistics r Scatterplot regression coefficient slope std error of regression coeff covariance correlation coefficient r r2 n Primary Ur Covariste C Enlarge Enlarge Press Enlarge to view a larger version of the Cross Variate Regression scatterplot From the Regression window you will be able to edit and print the graph as well as list graphed data values as described below 67 Chapter 5 Summary Statistics Cross Variate Regression The best test of whether a covariate is related to the primary variate a prerequisite for cokriging is to perform a regression analysis In GS the results of the regres sion of the primary variate Z vs the Covariate Z2 is presented in the Data Summary Regression tab Clicking the Enlarge command in that window brings up the Cross Variate Regression window Regression Cross Variate Ur x C nl Primary Ur
11. Files that store analysis parameters and data for a particular data set GS parame ter files typically have a par extension 165 Chapter 16 Glossary Polygons Polygons are Irregular shapes that can be interpolated or excluded from interpola tion during kriging Polygons are defined by at least 3 vertices coordinate pairs that define the polygon outline Polygons can be as complex as continent outlines or as simple as building outlines Posting A Coordinate Posting is a map of coordinate locations The location of each data point in the active data set can be marked by a symbol corresponding to its relative value Punctual Kriging A type of kriging that provides an estimate for a precise point Block kriging provides an estimate for a discrete area around a specific interpolation point Quotes as Column Title Separators Column or variate names are separated by quotes E G m east north ug g pH Range The range also called effective range is the separation distance over which sample locations are autocorrelated i e over which there is spatial dependence among sample locations In variogram models the range is calculated from the range pa rameter A isotropic models or A and A anisotropic models See model defini tions for further information Same as for Data Records The delimiter for column or variate titles is the same as specified for data records E G if the data records in a file
12. For files where there is more than one z variate per record a missing value for any field in the record means that the entire record will be treated as missing To avoid this problem use comma delimited data records Any of these parameters field delimiters number of header records missing value indicators etc can be changed to a custom format from the Import Text File window Note that some Surfer files are comma delimited rather than space delimited The following listing is the first 9 records of a standard Surfer input file that has fields for an x coordinate a y coordinate and one z variate Note the three var iate names in record 1 and the missing values in records 5 and 9 Xdata Ydata Zdata 4 5 119 0 42 2 7 29 4 0 45 1 6 32 6 0 08 44 5 0 6 64 0 14 2 4 71 8 0 32 7 8 3425 0 12 6 7 10 2 6 7 16 3 0 49 Chapter 4 Importing Data from External Files Spreadsheet and Database Input Files Choosing to import a spreadsheet database or HTML files from the File Import Dia log brings up a window similar to the one for Excel spreadsheets below Multiple worksheets or tables within the larger spreadsheet workbook or database are avail able through a pull down listbox The contents of the spreadsheet or data table are displayed in the large preview area When the OK button is pressed the contents of the file are read into the GS Worksheet according to rules specified by the Proper ties command A different dialog i
13. measured sample value at point h N h total number of sample couples for the lag interval h and s sample variance for all z s Standardized variograms both isotropic and anisotropic appear in the Autocorrela tion Window on the Standardized Variogram tab Pressing the Expand button on this tab brings up the Standardized Variograms window note the sample variance line at 1 0 along the y axis EETTUTITUTTIDENNUS ix Pb Isotropic Standarized Standardized Semivariance 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90 Degra 41 Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 96 Chapter 7 Other Autocorrelation Measures Madograms Madograms are similar to traditional variograms see Semivariance Analysis ex cept that the absolute difference between 2 and zi is used rather than the square of the difference as for traditional semivariance The formula thus becomes yuh 1 2N A X zi zin where Ym h semivariance M for interval distance class h z measured sample value at point Zin Measured sample value at point h and N h total number of sample couples for the lag interval h Madograms both isotropic and anisotropic appear in the Autocorrelation Window on the Madogram tab Press the Expand button on this
14. note the empty cells in the figure above To insert or delete a row or column in the worksheet use the Edit Insert command or Delete on the menu bar Column Assignments In the Data Worksheet window you may specify which field or column to associate with the Sample ID X Coordinate Y Coordinate the Z variate the Z2 variate or External Drift by clicking on the second cell from the top in any column This will bring up the Column Assignment dialog 39 Chapter 3 Working with Data Column 4 Assignment xj Column 4 name b _ Assign column 4 as C None C XCoordinate Z Primary Variate C Sample 1D Y Coordinate 22 Covariate C External Drift V Rebuild automatically when reassign Column name The name of the column or variate name Assign column as None make column unassigned Sample ID the specified column contains Sample Number or Sample ID in formation This can be text or numeric data X Coordinate the specified column contains values for the X Coordinate loca tion If you choose a column that is already assigned the other variate s col umn will switch with the original X Coordinate column Y Coordinate the specified column contains values for the Y Coordinate loca tion If you choose a column that is already assigned the other variate s col umn will switch with the original Y Coordinate column Z Primary Variate the specified column contains values for
15. the Mi nor Ranges and Major Ranges are calculated from and A respec tively as described in the formulas for the different models later in this chapter GS calculates default values for each parameter of the five models You may change any of these four model parameters from the Anisotropic Variogram Model dialog window 86 Chapter 6 Semivariance Analysis Overview Anisotropic Variogram Model Pb x Variogram Nugget Structural Variance Model Type Variance Co Sill Co C Range Minor Range Major Gaussian 0 214000 0 879361 155 5382 325 9720 amem lire cena s This Fit r AutoFit 34 Residual SS 0 429 0 429 r2 0 533 0 533 Proportion C Co C 0 757 0 757 Model Gaussian Gaussian Autofit Cancel Variogram Model Type Choose one of four isotropic models Linear Spherical Exponential or Gaussian As a model is chosen the variogram graphs will be updated to denote the change Model Terms Any of the three parameters for each model may be changed within the ranges al lowed for individual parameters To change a value either move the slider beneath it or type a new value directly into the text box Nugget Variance or Co the y intercept of the model the nugget variance can never be greater than the sill Sill or Co C the model asymptote the sill can never be less than the nugget variance Range Minor the separation distance over which spatial dependence is a
16. the sill never meets the asymptote in the Gaussian or exponential models Gaussian Model 0 254 a 0 191 5 t amp 0 127 E 0064 0 000 0 0 20 5 41 0 61 5 82 1 Separation Distance h 85 Chapter 6 Semivariance Analysis Overview Anisotropic Variogram Models Anisotropic variogram models are similar to those for isotropic variograms but in clude directional information in the range parameter GS calculates geometric ani sotropy in which the range changes with direction but the sill remains constant Consequently the anisotropic model includes a directional component only for the range term below Four types of anisotropic variogram models are provided in GS Linear Spherical Exponential and Gaussian Each model can be described using the following terms e Nugget Variance or Co the y intercept of the model this value is the same for all directions e Sill or C C the model asymptote this value is the same for all directions e Range or A the separation distance over which spatial dependence is ap parent for the direction examined It is the sum of range parameter for the major axis of variation and e A the range parameter for the minor axis 90 adjusted for the angle between pairs 0 as noted in the formulas for indi vidual models Sometimes Range or A is called the effective range in order to distin guish range from a model s range parameters A or Az In GS
17. unless the active window contains a graph You can also access this com mand by right clicking on a graph Data underlying maps can be displayed from the Map menu only from the map windows e Summary Statistics display basic statistics for the primary variate Z and covariate Z2 if defined e Frequency Distribution display frequency distributions for the primary vari ate Z and covariate Z2 if defined e Quartiles Posting display a posting map for the primary variate 2 and covariate Z2 if defined The Autocorrelation Menu The Autocorrelation menu provides access to one of several types of autocorrela tion analyses in GS GS Geostatistics for the Environmental Sciences Eile Edit Data Autocorrelation Interpolate Map Window Help ool Variogram RE gt uei Hae E Kl d Correlogram b Covariance Drift Fractal General Rel Variogram Madogram Moran s Pairwise Rel Variogram gt Primary Variate 2 Rodogram 1 Seconda ariate Z2 Standardized Variogram Cross Variate Z x Z2 B 9 e Variogram e General Relative Variogram e Correlogram e Madogram e Covariance Analysis e Moran sl Analysis e Drift e Pairwise Relative Variogram e Fractal Analysis e Standardized Variogram 19 Chapter 2 Getting Started For each analysis you may choose to analyze the primary variate Z the covariate Z2 or the cross variate Z x Z2 alt
18. 0 00 26 67 53 33 80 00 Separation Distance h Exponential model Co 0 31800 Co 2 64600 Ao 67 RSS 0 262 isotropic 0 Degrees lt 45 Degrees lt 90 Deor lt T gt seater Lag Class 7 995 pairs click for variance cloud Clicking on this variogram point or the Cloud button brings up the variance cloud for lag class 7 below and it becomes apparent that a number of pairs are very different from the others placing the cursor over each of the outlying points reveals that all of them contain record 4 as a member of the pair The cursor below is over the point represented by records 4 and 98 at a separation distance of 53 79 as noted at the bottom of the window iBixi Pb Variance Cloud Isotropic Lag Class 7 167436 O gg gan go r1 Records 4 and 98 d Click for details Variance 48 00 50 67 53 33 56 00 Separation Distance h EN m Cloud Pair 71 Records 4 and 98 separation distance 53 79 Clicking on this variance cloud point brings up the Sample Details window which 108 Chapter 8 Variance Clouds and h Scattergrams gives us the option to temporarily mask remove from the active data set one of the data records for this pair Sample Details x Head Record 4 Z value 13 000 Mask Tail Record 98 Z value 0 710 Mask Separation Distance Jh 53 79 Variance 151 04410 Since record 4 is a member of all of these outlier p
19. 1 25 2 813 1 801 0 789 0 223 Pb In Pb Plot Cumulative Frequency gt Plot Type of plot to graph Choose either Frequency Cumulative Frequency as dis played above or Normal Probability curves displayed below Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu Cumulative Frequency Values The Cumulative Frequency Listing window provides a listing of the values used to create the Cumulative Frequency Distribution graph All values in the data set are ranked by value ascending order any given row is the frequency of the value of that row plus all preceding frequencies expressed as percent the final cumulative frequency value is 100 For example the first value in the table is the lowest value in the data set and has a cumulative frequency of 100 x 1 n 58 Chapter 5 Summary Statistics Cumulative Frequency Values Trans o o Actions In Pb 0 781 1 563 2 344 3 125 3 906 4 688 5 469 6 250 7 031 7 813 8 594 9 375 10 156 10 938 11 719 10 xl Cumulative Frequency You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or u
20. 2 12 1 37 0 62 0 13 Covariate C Regression coefficient 0 878 SE 0 023 r2 20 960 y intercept 2 305 n 65 Primary Ur 2 26 Covariate C 0 09 Note that when the cursor is placed over a point the second point from the right in the graph above the data values for that point are identified at the bottom of the window Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu 68 Chapter 5 Summary Statistics Cross Variate Regression Values The Regression Listing window provides a list of the values used to create the re gression Regression statistics appear in the Data Summary Regression tab Regression Values Cross Variate Ur x ioj xj Record Primary Variate Covariate 2 1 933 0 5108 5 1 726 0 6733 8 1 384 0 9943 9 1 562 0 7765 11 1 335 0 9676 14 1 954 0 4943 15 1 866 0 4943 20 2 248 0 0943 24 1 022 1 4271 26 0 678 2 0402 34 1 560 0 9416 35 0 747 1 5606 36 1 366 1 0788 39 0 531 2 1203 43 1 082 1 3863 1 343 0 9943 44 amp 1627 0 8210 48 0 779 1 5606 Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Deci
21. 4 Number 1528 Define Xaxs Yaxs Zaxis Projection 3 d displays a 3 dimensional map of the data The height of the map can be adjusted by changing the 3 d Proportion the perspective can be adjusted with the Rotate Mouse Action command of the calling window 2 d displays a flat 2 dimensional map of the data 3 d Proportion for 3 d projections sets the height to width ratio of the map For tall skinny maps set this value to 2 or higher For flatter maps set to less than 0 5 This setting is not available for 2 d projections This command will not affect the as pect ratio of the map i e the x and y axes will remain proportional to one an other Map Surface Contour lines draws lines between contour intervals 33 Chapter 2 Getting Started Color bands fills the space between contour lines with different colors colors can be specified from the Define Contour dialog window by pressing Define Contour Levels below Smoothing apply slight smoothing to the data to improve visualization Solid pedestal for a 3 d map fill in the area beneath the surface with a solid color Wireframe for 3 d maps drapes an x y grid over the surface Wireframe Weave specifies the density of the wireframe grid A weave of 0 puts a grid line at every data row and column a weave of 1 skips one row column a weave of 2 skips 2 etc Contour Levels Number the number of contour levels to put on the m
22. 8 00 24 00 56 00 88 00 meast Graph Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu 127 Chapter 9 Interpolation Basics Cross Validation and Jackknife Analysis Cross validation analysis is a means for evaluating effective parameters for kriging and IDW interpolations Two types of validation are provided by GS Cross validation and Jackknife analyses In cross validation analysis each measured point in the spatial domain is individually removed from the domain and its value estimat ed as though it were never there Then the point is replaced and the next point is removed and estimated and so on In this way a graph can be constructed of esti mated vs actual values for each sample location in the domain In Jackknife analysis estimates are compared against measured values for a set of locations different from those used as input data Before performing jackknife anal ysis you must specify the jackknife data in a worksheet that appears when you press the Define command Cross validation and jackknife analysis are not available for Conditional Simulation ETTIDUTIITONENSSS 8i Actual Pb 0 060 0 457 0 853 1 250 Estimated Pb Regression coefficient 0 976 SE 0 111 r2 20 379 y intercept 0 030 SE Prediction 0 162 n 128 Record 100 actual value 0 17 estimated value 0 69 Each point on the
23. Chapter 2 Getting Started command Graph Settings Axis Scaling Tab The Axis Scaling tab of the Graph Settings Dialog Window allows you to specify how to scale the graph axes e g how long or short an axis should be and how the bars and symbols should look General Axis Tiles Labels Contour Detais X Axis r Y Axis 1 pPosting Symbols Numeric Range r Numeric Range I auto zero origin auto zero origin E user defined C user defined min 0 6 min 15 79 3 79 0 r Number of Ticks 1 Number of Ticks major ticks 4 major ticks minor ticks 2 z minor ticks 25 X Axis Range and Tick Marks The X Axis range can be set to automatic or user defined manual If the range is automatic and the lowest value in the graphed data set is greater than zero then the axis range is set to a minimum value of zero and a maximum value of 10 greater than the highest value in the data set If the range is automatic and the lowest value is less than zero then the axis range minimum is set to 1096 less than the lowest value The Number of Labels bar graphs only not shown above refers to the number of values placed along the x axis The Number of Ticks x y graphs and maps only refers to the number of ticks along the x axis Major ticks are accompanied by labels values minor ticks are not la beled and appear between major ticks To set the appearance
24. Hilgardia 51 1 75 159 Chapter 15 Bibliography Webster R 1985 Quantitative spatial analysis of soil in the field Pages 1 70 in B A Stewart editor Advances in Soil Science Volume 3 Springer Verlag New York Webster R and M A Oliver 2007 Geostatistics for Environmental Scientists Trends in Organizational Behavior John Wiley and Sons NY 304 pp 160 Chapter 16 Glossary Chapter 16 Glossary Ao Range parameter in variogram models The relationship of Ao to range A effective range depends on the model See specific model definitions for more information Range parameter for the major axis in anisotropic variogram models The relation ship of A to major range depends on the model See specific model definitions for more information A2 Range parameter for the minor axis in anisotropic variogram models The relation ship of A to major range depends on the model See specific model definitions for more information Binary Data Record Format Binary data from many spreadsheet and database programs can be imported direct ly if the file can be viewed using the View command then it can be imported Eligi ble files include Excel and Lotus 1 2 3 worksheets dBase Paradox Access etc A Character as Missing Value Indicator Specify the character to be used as a missing value indicator in the field that will ap pear when a character value is specified in the list box The example below pre sume
25. Relative Variograms The general relative variogram is a graph of semivariance standardized by the squared mean of the data used for each distance interval h yGR h y h m Mah where yGR h general relative semivariance for interval class h y h semivariance for interval distance class h m mean of all head values for lag A or 1 N h Zz and m n mean of all tail values for lag h or 1 N h 2 Relative variograms can be calculated only for data sets for which all Z values are positive otherwise the denominator above could equal zero If the minimum Z val ue in the active data is 0 then the relative variogram will not be drawn To avoid this problem you can first scale or otherwise transform the data in the Data Sum mary Window General relative variograms both isotropic and anisotropic appear in the Autocorre lation Window on the General Relative Variogram tab General relative variograms are not available if the minimum Z value is less than zero Press the Expand button on this tab to bring up the General Relative Variograms window 102 Chapter 7 Other Autocorrelation Measures General Relative Variograms Pb J 101 The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 103 Chapter 7 Other Autocorrelation Measures Pairwise Relative Variograms The pairwise relative variogram is a graph of semivariance normalized by th
26. Scattergrams above 65 Chapter 5 Summary Statistics Defining Posting Intervals The Define Posting Intervals window allows posting intervals to be custom defined and provides the opportunity to set symbol size color shapes and legend names This window is accessed from the Coordinate Posting window x Value Range Symbol Name Color Size B Hose ES o MA coU 2710 2770 me 7 24 mean caty cuarties Value Range Specify the upper threshold of each value range Changing a Percentile or Intervals value will change the Type of Level defined in the Coordinate Posting window to Custom The number of values displayed is based on the number of Levels chosen in the Coordinate Posting window Symbol Choose a symbol from the drop down list for the specified interval Name Choose a name to appear in the chart legend Color Choose a color for the specified symbol by clicking on the colored box Size Choose a size for the specified symbol Legend title Specify the title to appear at the top of the legends No legend will appear if only 1 interval level is chosen Posting Sample Details The sample details window pops up when you click on a point in the 1 d or 2 d Co ordinate Posting window 66 Chapter 5 Summary Statistics xi Record Number 47 Sample ID 47 00 X Coordinate 26 20 Y Coordinate 73 30 Z Pb 0 54 Transformed 0 432
27. Select Column Select Cti A Toolbar Cut remove selected material to the clipboard Copy copy selected material or graph if graph window to the clipboard You can also access this command by right clicking on a graph or worksheet Paste paste the clipboard into the selected area Delete delete selected material Edit Graph edit the graph in the active window If there is not a graph in the active window this command will be dimmed You can also access this command by right clicking on a graph Select Select a worksheet row or column If the cursor is not in a worksheet this command will be dimmed Toolbar customize the toolbar to contain a variety of different tool shortcuts 17 Chapter 2 Getting Started The Data Menu The Data menu provides access to the data worksheet and to summary statistics windows and provides commands for importing and exporting data files and for ma nipulating data within the worksheet GS Geostatistics for the Environmental Sciences Demo2d 2Dimensional File Edit Data Autocorrelation Intepolate Map Window Help fF Worksheet E E3 ls x Assign Column P Bt Sot Change Decimals b Insert b Delete b amp Import Data text or binary file Export Data Summary Statistics b Frequency Distribution b Quantiles Posting 4 Primary Variate 2 e WorkSheet d
28. Simple kriging assumes the expectation of the random field to be known and relies on a covariance function Stationary simple kriging has a constant mean which in GS is calculated as the mean of the input data Z In non stationary simple kriging a locally varying mean is specified for every interpolation grid point using the Define command For continuous variables indicator kriging estimates the probability that the interpo lation point is greater than a particular cutoff value specified by the user Variogram Variogram models for isotropic and anisotropic variograms are defined and chosen using the Model command in the Autocorrelation Analysis window Here in the Kriging window you can specify whether to use the isotropic or anisotropic model You can also choose to use a relative variogram in which the nugget and structural components are rescaled from 0 to 1 0 Discretization grid Choose either Point or Block kriging in this section Your choice should be made on the basis of sampling design and variate characteristics If samples were taken to represent an area around the actual sample point e g if samples from an area around the sampling coordinate were composited before analysis then block kriging may be more appropriate than punctual If samples were taken to represent point values then punctual kriging will be more appropriate For block kriging you must define the discretization grid also called the local grid which
29. Simulations In conditional simulation the number of simulations used to produce estimates of Z can strongly affect the outcome of the interpolation Below are maps of an 80 x 80 m grid interpolated at a density of 0 5 m with different numbers of simulations Below left is a map of block kriged data on the right is the same data interpolated by condi tional simulation n 1 simulation Additional simulations improve clarity the map below left represents 10 simula tions below right n 100 simulations mo ano E 400 HE E 200 00 00 200 LII wo 900 meat And still more simulations resolve further detail The map below left represents n 1 000 simulations below right n 10 000 simulations wo ao 20 T T m mo wo ome mo You may wish to set the number of simulations high enough that additional simula tions reveal little further resolution mnerth 134 Chapter 11 Kriging and Cokriging Chapter 11 Kriging and Cokriging Kriging provides a means of interpolating values for points not physically sampled using knowledge about the underlying spatial relationships in a data set to do so Variograms provide this knowledge Kriging is based on regionalized variable theory and provides an optimal interpolation estimate for a given coordinate location GS performs several types of kriging The Interpolation Window contains the Krig tab Krig cokrig simulate ow
30. Window Global Reset Sets all user default values on all tabs to original GS defined default values Save Exit Close window and keep preference changes 24 Chapter 2 Getting Started User Preferences Data File Import Tab The Preferences Data File Import dialog window allows you to set user default values for importing data files into the GS Data Worksheet General r Default Settings for Data File Imports Filename extension gat Default columns for Sample ID 0 X Coord 1 Y Coord 2 Z Variate 3 Covariate 4 Ext Drift 0 Places past ndi custom 1 decimal to show 234 Automatically Rebuild Data Arrays when M import new data Make new column assignments Global Reset Cancel Savetxt Reset The Reset command returns all user default values on this tab to original default values To reset all values on all tabs use the Global Reset command at the bot tom of the window Filename Extension Default extension for the data file name specified when importing data files to the Data Worksheet Default Columns When importing data files these values indicate which columns or fields to assign initially to different variates Column assignments can be changed in the Data Work sheet window Default Import File Type When importing data files this file type will be the default type specified See Import File Types later for a description of spec
31. be either round or elliptical if elliptical the angle of the el lipsoid in addition to its width and length must be specified the default angle is the same as the anisotropic axis orientation used for semivariance analysis Additionally you may specify an octant search in which the geographic neighbor hood is divided into 8ths and only a limited number of neighbors within the octant are used for interpolation This is useful when there are many more neighbors on one side of an estimation location than on another and there is a danger of using a disproportionate number of neighbors from that side An octant search limits the number of neighbors that can be used from any given octant When cokriging you may specify a separate set of search criteria for the covariate Z2 These criteria are set on the Covariate tab of the Search box Interpolation Type Krig Cokrig Simulate or IDW You may choose to interpolate using either Kriging Cokriging Conditional Simula tion or IDW Inverse Distance Weighting by choosing one or the other tabs on the right hand side of the window the options on each tab are described in the next sec tion Calculate Perform interpolation analysis During analysis values are written to the output file in the specified format You can stop analysis by pressing the Escape key or the Cancel button on the progress bar Validation Two types of validation are provided by GS Cross validation and Jac
32. cannot be selected Window Menu The Window menu allows you to quickly move to open windows GS File Edi Data Autocorrelation Interpolate Window Help OSES tms So Ed tS z E Data Worksheet Data Summay E Primary Variate Z Secondary Variae Z2 Map Cross Variate Zx Z2 Cascade rearrange all open windows Data Worksheet display data worksheet window Data Summary display data summary window for the primary or secondary variate Autocorrelation Analysis display autocorrelation windows for the Primary Var iate Z Secondary Variate Z2 or Cross Variate Z x Z2 Interpolation display kriging conditional simulation and IDW analysis window Map display mapping window The Help Menu The Help menu provides access to GS help functions 21 Chapter 2 Getting Started 22 File Edit Data Autocorrelation Interpolate Map Window Help Oa ES g BB St ts z 5 Check for 65 Update via Internet E How to Contact Gamma Design Software eg Email Gamma Design Software fat Go to www gammadesign com F Register On line XX Deactivate About Gs GS Help display context sensitive help topic Check for GS Update send an automatic query to www gammadesign com to see if the version of GS currently running has been updated If a newer ver
33. colors for the intervals are the same as they would be if 15 intervals were checked If on the other hand the Dynamic box is checked the colors for the inter vals are adjusted such that interval 10 becomes the color of the original interval 15 Checking this box provides greater color contrast on maps Invert Flips the color range This allows you to associate the highest interval values with the darkest colors or vice versa Cancel Exit the dialog window without saving changes 151 Chapter 14 Mapping Map Image 3 d The 3 d map image is produced by the Draw command from the Mapping window Pb 0 727 0 687 0648 0608 0569 0 529 0 490 0 450 0 411 0 371 0 332 0 292 0 253 0 213 0 174 0 134 Mouse Location Bl xl Mouse Action Reset X 62 9 Y 58 7 Z 0 552 Mouse Action Off returns the mouse to normal operation Rotate turns the cursor into a rotator cuff when the left mouse button is pushed allowing the image to be rotated as desired Move allows the graph to be moved within the window by clicking the left mouse button and dragging the cursor Scale shrinks the graph image with the left mouse button Zoom allows you to zoom in on a graph area by using the left mouse button to define a rectangular zoom area Within the zoomed area the location of the cursor is noted on the Mouse Location panel Reset resets the image to th
34. constrain values 119 cross validation analysis 121 129 discretization grid 137 140 distance interval 123 draw map after interpolating 28 grid 119 indicator kriging 137 interpolate locations 125 interpolate menu 20 inverse distance weighting 117 141 irregular grid 119 124 jackknife analysis 121 129 kriging 117 136 kriging with external drift 137 kriging with trend 136 masks 119 See Polygons menu 20 nearest neighbors 120 neighborhood radius 121 normal distance weighting 117 141 number of points 123 octant search 121 optimize range 123 order of output 28 ordinary cokriging 140 ordinary kriging 136 output defaults 28 output file formats 119 output files 119 output standard deviation 120 output variance 120 polygons 119 126 punctual cokriging 140 punctual kriging 137 range 118 123 regular grid 118 122 relative variogram 137 140 172 search neighborhood 120 simple cokriging 140 simple kriging 137 specific shapes 119 standard deviation 28 standardized ordinary cokriging 140 type 121 universal kriging 136 validation 121 129 variance 28 120 variogram model 132 137 140 window 118 Z estimate boundaries 122 Interval class 70 Inverse distance weighting 117 121 141 Irregular interpolation grid 119 124 Isotropic variogram models 79 Jackknife analysis 121 129 values 131 worksheet 121 Kriging 117 121 136 ouput standard deviation 120
35. field for 2 dimensional analyses and the field column that corresponds to the Z variate For cokriging you will also need to as sign a field to hold the covariate Z2 values Field assignments are performed by clicking on the top row of the Worksheet to bring up a Field Assignment dialog win dow Data Records Data Records are records in text files that contain data values Data records follow header records that contain descriptive information about the file Data records are imported into the GS Worksheet header records are imported into the Data De 163 Chapter 16 Glossary scription portion of the Worksheet Window Decimal Point Missing Value Indicator In the record below the third value appears as a decimal point and will be read into the worksheet as a missing value 13 2 34 5 0 15 Discretization Grid The discretization grid describes the size of the grid placed around the interpolation point when block kriging The estimate for the interpolated block is based on the mean value of estimates for each of the discretization grid points A single discreti zation point describes punctual kriging A 2x2 grid averages 4 grid points Larger discretization grids take longer to interpolate Effective Range See Range Geo referenced Data Geo referenced data are data that have been collected from a specific location i e any data for which there is a spatial coordinate associated with each data value Header R
36. files the standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format Also for this format the x and y interpolation intervals must be the same you can set them to be the same from the Interpolation Grid dialog window This format is compatible with ESRI s ArcInfo Geographic Information System Data in this format can be imported directly into ESRI s Arclnfo or ArcView Note that this format is different from the ArcView XYZ Input File format described earlier which is an ArcView output format that can be read by GS The following listing is for the first 200 or so coordinates a standard Arc Info or ArcView format krig output file ncols 376 nrows 253 xllcorner 185556 375 yllcorner 127261 5234375 cellsize 1009 975 NODATA value 999 354 314 309 301 286 264 305 306 285 285 268 314 339 306 266 248 252 240 256 282 277 289 269 285 277 258 256 282 268 246 250 249 245 266 262 287 295 335 325 323 359 369 361 357 394 450 407 409 382 409 394 486 510 502 516 546 531 542 572 579 586 594 522 654 550 615 678 709 616 533 430 576 507 638 778 769 456 432 576 635 778 721 769 869 563 589 640 588 770 833 874 1019 965 933 621 795 1131 1044 899 1072 1112 880 910 1069 1088 1071 965 975 902 800 543 350 330 376 310 384 418 352 263 205 202 200 200 201 200 198 201 201 201 201 201 201 694 695 To convert this file to an ArcGIS grid file use ArcToolbox either the light ver sio
37. for example variogram models you may specify line pattern width and color Graph Colors Borders Graph Title A title is text that appears at the top center of the graph area To change the font of the title press Change which will bring up a Font Dialog Window Graph Legend The legend appears on maps and quantile postings to indicate the value ranges for different symbols or colors Legend text appears at the top of the legend table To change the font of the legend title and values press Change which will bring up a Font Dialog Window Graph Footnote A footnote is text that appears at the bottom left of the graph area To change the font of the footnote press Change which will bring up a Font Dialog Window To have variogram model parameters printed as a footnote to variogram graphs place in this field the exact phrase model results do not include quotes This notation is placed in the field by default whenever a new variogram and model are calculated you will need to remove it if you do not want variogram model parameters to appear as a graph footnote Apply Now Press Apply Now to apply any changes made to the graph and keep the Graph Set tings dialog window open Exit Cancel Press Exit to close the Graph Settings Dialog window Any changes made since the last Apply Now command will be applied to the graph Press Cancel to exit the Graph Settings Dialog without applying any changes since the last Apply Now 30
38. from the Activation Screen above the following Acti vate GS window will be displayed Activate 65 GS Activation Please enter your name Please enter your organization Please enter your serial number Please enter your license number activation code Buy now online Advanced Help Back Name Organization Enter your name and organization Serial Number Enter the serial number for your copy of GS Find this number on the CD sleeve or in the confirmation email you received after purchasing a downloaded copy of GS It will start with a letter License Number activation code Enter the license number also called activation code This number is on the CD sleeve or in the purchase confirmation email that you received Chapter 2 Getting Started Buy now online Launch a web browser pointed to www gammadesign com that allows you to pur chase a license Advanced Bring up an advanced activation dialog that allows you to activate through a web browser on another computer or to use a proxy server to connect to the internet Continue Continue with activation Activation Advanced Options This dialog provides the option for providing a proxy server address for accessing the internet during activation or for activating over the web using this or another computer Activate GS Advanced Options Use Proxy Server Activate over web Identify Proxy Server IF your internet ac
39. h Spherical model Co 0 01870 Co C 0 05590 Ao 80 00 RSS 1 215E 04 Isotropic 0 Degrees 45 Degrees 90 Degre gt Scatter Right click to edit list print etc or click point for variance cloud Re examination of the variance cloud for lag class 7 below reveals that the highest y axis values are substantially lower than before 1 31 vs 13 65 and more im portantly all of the major outlier pairs are gone This was accomplished by removing a single data record from the analysis igi xd Pb h Scattergram Isotropic Lag Class 7 jaa gp 15 r1 Head Value Tail Value La a Cloud Scatter Right click to edit list print etc or use mouse to identify points The right click menu and other commands work here as they do for the Variograms Window 114 Chapter 8 Variance Clouds and h Scattergrams h Scattergram Pairs This read only window contains a listing of all pairs of points within a specific lag class including for each pair the difference separation distance and the identity data record number of each member of the pair These pairs are graphed in the h Scattergram window Note that in the example below sorted by difference with pairs of greatest differ ence listed first record 4 shows up as a member of 14 high difference pairs This confirms the record as an outlier as was found in the h Scattergram above ixi Levi A di Neu Distance h Di
40. in the Interpolation window 5 C Program Files GSWin70 Demo2d krg 745766 bytes 55 Output Block Kriging Interpolation File v7 0 Set Dimensions 2 Interval source Calculated Interpolation interval x y 0 5000 0 5000 X coor m east range 0 0000 80 0000 m north range 0 0000 80 0000 Z est Pb range 0 152 0 790 Z sd Estimation Standard Deviation range 0 000000 0 136926 Mean Z estimate sd 0 38866 0 018223 Valid N 25921 Missing N 0 Missing Value Indicator 99 X Coordinate Y Coordinate Z Estimate EstStdDev n 0 00 0 00 0 521 0 1357 16 0 00 0 50 0 521 0 1337 16 0 00 1 00 0 548 01329 16 0 00 1 50 0 547 0 1307 16 x nnan rar manor Data Append Dialog When importing data into the Data Worksheet if the worksheet already contains da ta then you will asked how to import the new data whether the imported data should Replace the existing data be placed in columns to the right of the existing data Append to Side or be placed at the bottom of the worksheet Append to End Cancel will cancel the import with no changes to the worksheet 65 File Alert xi The current worksheet is not empty do you want to append new data to the end concatenate new data to the side or replace the existing worksheet Append to Side Cancel Append to End Help 53 Chapter 5 Summary Statistics Chapter 5 Summary Statistics Data Summary Window
41. it will remain activated until you choose to deactivate it You will want to deactivate it if you move GS to a different computer To Deactivate GS prior to moving the license to a different computer use the Deac tivate command on the Help menu You do not need to deactivate GS prior to rein stalling Windows or reformatting your hard drive GS may be deactivated and re activated an unlimited number of times When you first launch GS the following activation screen will be displayed Welcome to GS Version 9 Please activate your copy of 65 Activate GS now 1 have a serial number ready to enter Buy now online Evaluate GS am not yet ready to activate Hep _ Cancel Acivation Options 1 Activate GS now have a serial number ready to enter Choose this option if you have purchased GS and have a 15 digit license number activation code from the CD sleeve or from the purchase confirma 7 Chapter 2 Getting Started tion email 2 Evaluate GS am not yet ready to activate Choose this option if you want to remain in evaluation mode You will have the number of days specified in the dialog narrative to purchase a license If this option is not available if it is disabled as in the illustration above then you have run out of evaluation days and must purchase a license in order to continue Continue Continue to the Activate GS window How to Activate If you choose to Activate Now
42. may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 130 Chapter 10 Conditional Simulation Chapter 10 Conditional Simulation Conditional simulation is an advanced interpolation technique whereby Z estimates are based on a form of stochastic simulation in which measured data values are honored at their locations Other interpolation methods including kriging and IDW will smooth out local details of spatial variation especially as interpolated locations become more distant from measured locations This can be a problem when you are trying to map sharp spatial discontinuities such as contamination hotspots or fault lines GS uses a sequential Gaussian simulation method The Interpolation Window contains the Simulate tab r Variogram Model isotropic Anisotropic r Output Estimated Z C Probability Zest gt t 0 19 r Analysis No of simulations 1000 Use different seed 3 Multigrid refinements 24 r Secondary Data None Residuals C External drift Define C Variogram Model Variogram models for isotropi
43. model is similar to the exponential model but assumes a gradual rise from the y intercept The formula used is y h Co C 1 exp h where y h semivariance for interval distance class h h lag interval Co nugget variance gt 0 90 Chapter 6 Semivariance Analysis Overview C structural variance gt Co and A 0 Az sin 1 range parameter for the major axis In the case of the Gaussian model the range or effective range for the major axis 39 A4 A range parameter for the minor axis 90 In the case of the Gaussian model the range or effective range for the minor axis 3 Ao angle of maximum variation angle between pairs Chapter 6 Semivariance Analysis Overview Anisotropic Semivariance Surface 2 d Variogram Map The Anisotropic Semivariance Surface or Variogram Map provides a visual picture of semivariance in every compass direction This allows one to more easily find the appropriate principal axis for defining the anisotropic variogram model A transect in any single direction e g 10 degrees north is equivalent to the variogram in that di rection the surface z axis is semivariance the x and y axes are separation dis tances in E W and N S directions respectively The center of the map corresponds to the origin of the variogram y h 0 for every direction See Isaaks and Srivastava 1989 page 150 and Goo
44. pressing De fine Contour Levels below Smoothing apply slight smoothing to the data to improve visualization Solid pedestal for a 3 d map fill in the area beneath the surface with a solid color Chapter 14 Mapping e Wireframe for 3 d maps drapes an x y grid over the surface e Wireframe Weave specifies the density of the wireframe grid A weave of 0 puts a grid line at every data row and column a weave of 1 skips one row column a weave of 2 skips 2 etc Contour Levels e Number the number of contour levels to put on the map e Define brings up the Map Contour Intervals dialog window described in greater detail below that allows you to set break points for individual inter vals and colors for contour bands Map Legend Show legend displays the contour legend next to the map Continuous vs Stepped display legend as continuous scale with values next to break points e g between color bands or display legend as stepped format with values next to boxed colors Ceiling e Contour lines project contour lines above the plot surface 3 maps only e Color bands project color bands onto the ceiling of the plot 3 maps only Floor e Contour lines project contour lines under the plot surface 3 d maps only e Color bands project color bands onto the floor of the plot 3 maps only Grid Lines e X axis place a vertical grid line along the back walls of the 3 d plo
45. provide a means for detecting outlier pairs of points that may be artificially skewing the vario gram You can use the mouse cursor to identify the number of pairs in specific lag classes reported at the bottom of the window in the example below the cursor was over the 2 symbol in the variogram and to begin variance cloud analysis Note also that parameters for the variogram model if present are presented in a graph foot note If you do not want parameters to appear as a footnote you must use the Edit Graph command to bring up the Graph Settings dialog and in the Footnote field re move the notation model results 515 Pb Isotropic Variogram 0 377 0 283 0 189 0 094 Semivariance 0 000 0 0 26 7 53 3 80 0 Separation Distance h Spherical model Co 0 1237 Co C 0 3504 Ao 59 20 rz RSS 2 973E 03 Isotropic 45 Degrees 90 Degre 41 Scatter Lag Class 2 637 pairs click for variance cloud Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu Cloud Scatter Create a Variance Cloud or Scattergram graph for a particular lag interval in a sepa rate window described in greater detail later 77 Chapter 6 Semivariance Analysis Overview Semivariance Values In this worksheet are listed for each lag class the average separation distance for pairs of points in that class the av
46. range parameter for the minor axis 90 In the case of the exponential model the range or effective range for the minor axis angle of maximum variation angle between pairs 89 Chapter 6 Semivariance Analysis Overview Linear Anisotropic Model The linear anisotropic model describes a straight line variogram Note that there is no sill in this model the ranges for the major and minor axes are defined in terms of the distance interval for the last lag class in the variogram The formula used is y h Co h C A where y h semivariance for interval distance class h h lag interval Co nugget variance gt 0 C structural variance gt Co and A V A cos 0 0 range parameter for the major axis In the case of the linear model there is no effective major range spatial autocorrelation occurs across the entire range sampled in GS model windows A is set initially to the separation distance h for the last lag class graphed A range parameter for the minor axis 90 In the case of the linear model there is no effective minor range spatial autocorrelation occurs across the entire range sampled in GS model windows is set initially to the separation distance h for the last lag class graphed angle of maximum variation angle between pairs Gaussian Anisotropic Model The Gaussian or hyperbola anisotropic
47. rather will provide a starting point for further exploration Automatically make anisotropic surface map the Surface Map com mand on the Semivariance Window will be automatically called after vario grams are calculated This will make the exploration of anisotropic relation ships more automated but there is a performance penalty as creating a sur face map requires further computation Number of lag intervals The active lag distance is divided into a number of different lag intervals classes for analysis The number of classes chosen initially by default is specified here During semivariance analysis the num ber of lag intervals will change as a function of the Active Lag divided by the Lag Class Distance Interval see Autocorrelation Analysis later Automatically subsample large data sets very large data sets can take hours of cpu time under certain conditions Check this box to randomly sub sample the data set during autocorrelation analysis only When this box is checked and the data set being analyzed has more than the specified num ber of subsamples only that number of subsamples are used in the autocor relation analysis Locations used in the analysis are randomly selected and each subsampled location is compared against every other location in the data set regardless of whether the other location was also selected as a subsample in this way there is no bias against small distance intervals due to subsampling
48. set you should try different steps for every set The number of lag classes and therefore plotted points in a variogram is a function of values for the active lag and the active step a 300 m active lag with a 15 m active step will have ca 20 lag classes Note however that the lag distance for a given class will be the average distance separating points within the class and not necessarily the midpoint for the class For a 10 20 m lag class e g the average lag distance may be 12 3 m rather than 15 m if more pairs of points are separated by 10 15 m intervals than by 15 20 m intervals Changing the distance interval will clear results on the screen from previous analyses calculated with a different step Results based on the new step must be re generated with Calculate command 72 Chapter 6 Semivariance Analysis Overview Anisotropic Axis Orientation Anisotropy refers to a direction dependent trend in the data Consider data collected from a two dimensional grid on a mountain slope elevation will be autocorrelated differently in the upslope downslope direction than in a cross slope direction and thus an isotropic all direction analysis may hide much of the autocorrelation that in fact is present Anisotropic analysis allows you to see if your data have a directional component that might arise from a variety of unforeseen factors Anisotropic analy sis is irrelevant for single dimension data such as a transect GS evaluates
49. that average the values of nearby sampled points to more complex tech niques like kriging that use in the average weights based on distance to nearby sample points and the degree of autocorrelation for those distances GS provides four broad types of interpolation All are nearest neighbor techniques in which values at locations close to the interpolation point are used to estimate the interpolation point value They differ in the way that nearby locations are weighted and interpolations calculated The four techniques are Kriging in which interpolation estimates are based on values at neighboring lo cations plus knowledge about the underlying spatial relationships in a data set Semivariograms provide knowledge about the underlying relationships The es timated value at a given location is a weighted moving average of best esti mates calculated to minimize local area variance There are a number of differ ent types of kriging described below Cokriging in which kriging interpolations include a covariate that is related to the primary variate and is measured at more locations than the primary variate In cokriging there is a variogram for the primary variate for the covariate and for the cross variate Conditional Simulation in which interpolations are based on a form of sto chastic simulation in which data values are honored at their locations This means that local details are not obscured by smoothing as they are in kriging In
50. there is no kriging solution Variate to Map Z values maps the estimated Z values in the file Z standard deviations or Z estimation variance maps the estimation Z vari ance or standard deviations in the file only files in the GS format contain both Z values and Z standard deviation or Z estimation variance values Sample Posting map only the original sample locations Requires the presence of a posting file which has the same name as the input file but a pos extension This file is created during interpolation if it is not present you will not be able to map a sample posting Coordinate Postings Quantile Plots of the active data are viewed through the Data Summary X Y Coor dinates Tab window described earlier Graph Type 2 d displays a flat 2 dimensional map of the data 3 d displays a 3 dimensional map of the data The height of the map can be adjusted with the Edit Graph command of the Map window the perspec tive can be adjusted with the Rotate command of the Map window 1 d displays 1 dimensional data e g a geographic transect or a time se ries as an x y graph This choice is not available for 2 dimensional data Show legend displays the contour legend next to the map Surface 148 Contour lines draws lines between contour intervals Color bands fills the space between contour lines with different colors col ors can be specified from the Define Contour dialog window by
51. values csv Excel spreadsheets xls html files htm and xml files xml Column titles are exported along with data except when exporting a re gion of the worksheet by first highlighting a block of cells To export the entire worksheet without column titles use Edit Select all before exporting Using Older Version GS Files The Convert File Dialog When loading a parameter par file created with a legacy DOS version of GS you will be queried to convert the DOS file to a GS Windows file 35 Chapter 2 Getting Started Convert File x File D YGEOSTAT1GS23c Files DEMO PAR appears to be a GS N DOS file press OK to convert to a GS Windows file and recalculate base statistics X Make backup old Help Cancel Make backup Check this box to make a backup of the file before converting The backup copy will have the same name as the original file but with the extension old E G a file named mydata par will be copied to a file called mydata old prior to the creation of the new Windows compatible mydata par If an error occurs during conversion the original file will remain intact and the backup copy will not be made 36 Chapter 3 Working with Data Chapter 3 Working with Data The Data Worksheet Window The Data Worksheet contains the data for GS analyses Data can be entered manually or can be imported via the Import file command Entered data can be edited filtered bounded and can be te
52. with four data columns are formatted with as a delimiter m east m north Pb ug g pH Sample ID The Sample ID is text or a numeric value that identifies a particular data record It is optional To specify a Sample ID column click on the top row of the data worksheet Sill or Co C The Sill of the variogram model C represents spatially independent variance Data locations separated by a distance beyond which semivariance does not change i e after the model asymptote or sill are spatially independent of one another Theoretically the sill is equivalent to sample variance 166 Chapter 16 Glossary Space Separated free format Values Values within data records are separated by spaces e g 13 2 34 5 35 6 0 15 Spaces as Column Title Separators Column or variate names are separated by spaces note that this option limits col umn titles to single words e g east north Pb pH Tab Separated Values Values within data records are separated by tab characters denoted by tab in the example below this format is often called tab delimited output by spreadsheet pro grams e g 13 2 tab 34 5 tab 35 6 tab 0 15 Tabs as Column Title Separators Column or variate names are separated by tab characters e g m east tab m north tab Pb ug g tab pH Transformation A transformation is a formula applied to all Z or Z2 values in a data set usually to better normalize its distribution Th
53. with values into cells with missing values and vice versa X Y Coordinates X Y coordinates describe a physical location at which a Z variate is measured The coordinates are presumed to be in Cartesian space i e with a 0 0 origin that in creases for x in an easterly direction and decrease in a westerly direction and for y increase in a northerly direction and decrease in a southerly note that values can be less than or greater than 0 Thus a value of 10 20 means 10 units east of the origin and 20 units north In GS if a Y Coordinate Column is not specified the data are assumed to be 1 dimensional i e collected along a transect or through time To specify or remove a Y Coordinate column click on the top row of the worksheet Note also that latitude and longitude are not part of a Cartesian coordinate system because coordinate distances measured in degrees represent different physical distances measured in meters in different places on the globe For a rough con version from latitude and longitude to meters consider that one second of latitude equals 30 92 meters on the ground for longitude calculate the cosine of the latitude then multiply by 30 92 Z Variate Data Z The Z Variate is the variate being analyzed and mapped e g elevation for a topo graphic map pH for a map of soil acidity chlorophyll content for a map of lake productivity population density for a map of rural population growth etc A Work sheet can
54. 0 and 10 0 Optimize The Optimize command sets the number of points to 61 for both the X and Y direc 122 Chapter 9 Interpolation Basics tions 101 points for a single dimension transect and calculates the appropriate Dis tance Interval The Interpolation Range is not affected Defining an Irregular Interpolation Grid Specify in this worksheet the locations of individual points to be kriged This method of specifying interpolate locations is appropriate when locations are not regularly spaced across the interpolation area If interpolate locations are regularly spaced regardless of whether the area is rectangular or a complex polygon it is usually more efficient to use a Regular Interpolation Grid Note that with either this Irregular Grid or the Regular Grid polygons can be used to exclude or include specific com plex shapes specify the shape of the polygon from the Krig window see Define Polygon Outlines later in this chapter X Coord Y Coord m east 450 11 90 2 70 29 40 32 60 44 50 64 00 71 80 3 50 10 20 16 30 27 20 42 70 51 10 63 30 65 60 77 4025 Block Size For Block Kriging this is the size of the block around each point that will be kriged The local discretization grid is placed within this block For regular grids block size is defined by the interpolation grid size For irregular grids it must be specified here For Point or Punctual Kriging and
55. 1 0 14 6 2 4 71 8 0 34 0 32 7 7 8 3 5 Qu37 Qx 12 8 6 7 10 2 0 61 99 00 9 6 7 16 3 0 46 0 49 47 Chapter 4 Importing Data from External Files Text Input File Formats GeoEas Format The standard GeoEas input file format is comprised of header records and data records Q Data records are comma or space delimited XYZ type data This means that each data record contains at least 3 fields an x coordinate location a y coordinate location and the value for at least one z variate measured at that x y location single dimension transects will have only x coordinate and z variate values Additional fields can hold a sample ID value and multiple z variates for a particular x y location Q Header records precede the data records and contain specific information about the data records Record 1 contains text of the user s choice usually a data set title or file name Record 2 contains the number of fields values in each data record Record 3 contains the name of the first field Records 4 contain the names of the second third etc fields one name per record Q There are no missing value indicators in the standard GeoEas format Q Any of these parameters field delimiters number of header records missing value indicators etc can be changed to a custom format from the Import Text File window Q The following listing is the first 11 records of a standard GeoEas input file that has fields for sample ID x coordinate y co
56. 2015 Table of Contents Table of Contents Chapter 1 Introduction OVOIVIOW Ll Sine cC et 1 System Requirements nennen 2 Installation and S 2 Updates tete LORD Een 11 s sedile toe eei RIED eee SEL 12 Single User License Agreement ssssssssseeeeees 12 Chapter 2 Getting Started From Data to Maps How to 14 General Screen Layout ssssssssssssseeeeeee enne 14 Menus nee e ed etg tende 15 User Preferences 2 c 4elii sleidc dulce ngon ee cnt 22 Graph Settings t dde Ero RE Ege c Lek Pe ead 28 Printing Copying and Exporting 34 Printing Copying and Exporting Worksheet Data 34 Using Older Version GS Files 34 Chapter 3 Working with Data The Data Worksheet Window eene 36 Column Assignments iiaeia aaa aa entere 38 Covariate Values Warning sse 40 Missing Values etri bo i tn 40 Data 1 tete 41 Duplicate Values rco mer teme emeret ers 42 Chapter 4 Importing Data from External Files File Import Dialog 5 re teme eatem ecce 43 Importing Text FeS niae 44 Text Input File Formats E ted E A A 46 GOOEAS AE E EA 47 ArcView XYZ eane eei aaia ba 48 S
57. 31 Cross variate regression 67 68 69 Cross variograms 20 95 139 csv files 18 35 52 Cumulative frequency distribution 170 graph 55 58 values 58 Data append dialog 53 bounding 42 builds 164 copying 35 exporting 35 fields 39 164 file import 44 52 filter 38 42 input file format 45 47 menu 18 records 38 47 48 49 50 52 164 summary window 62 67 regression analysis tab 67 X y coordinates tab 62 summary window Z tab 54 title 38 worksheet 37 Data file import 25 Database input files 44 51 Deactivate 22 Deactivation 7 11 activation code 11 license number 11 proxy server 11 Decimal places 18 24 26 39 Define posting intervals 66 Delete 18 Descriptive statistics 55 Discretization grid 124 137 140 165 Distance interval 123 DOS GS files 35 Drift 39 99 Duplicate values 43 55 Edit menu 17 Effective range 79 167 168 Email 22 Estimation variance 120 Estimation variance map 154 Excel files 51 Exclusive polygons 119 126 128 Index Exponential anisotropic model 89 Exponential isotropic model 83 Export data 18 35 graphs 17 35 External drift 39 assignment 40 Field column assignments 37 38 30 default assignments 25 delimiter 52 names 38 File extensions 35 75 120 143 144 145 146 148 166 import command 37 import dialog 44 import properties 51 52 view window 53 File menu 16 File view window 53 Filtering d
58. 31 333 341 Cressie N 1985 Fitting variogram models by weighted least squares Mathe matical Geology 17 563 586 Cressie N A C 1991 Statistics for Spatial Data John Wiley New York USA David M 1977 Geostatistical Ore Reserve Estimation Elsevier Scientific Pub lishing Co Amsterdam The Netherlands Deutsch C V and A G Journel 1992 GSLIB Geostatistical Software Library Oxford University Press New York Goovaerts P 1997 Geostatistics for Natural Resources Evaluation Oxford University Press New York Griffith D A 1987 Spatial Autocorrelation A Primer Association of American Geographers Washington D C 86 p Haan C T 1977 Statistical Methods in Hydrology lowa State University Press Ames lowa Isaaks E H and R M Srivastava 1989 An Introduction to Applied Geostatis tics Oxford University Press NY Chapter 15 Bibliography Journel A G and C J Huijbregts 1978 Mining Geostatistics Academic Press New York Krige D G 1966 Two dimensional weighted moving average trend surfaces for ore evaluation Journal of the South African Institute of Mining and Metallurgy 66 13 38 Krige D G 1981 Lognormal de Wijsian geostatistics for ore evaluation South African Institute of Mining and Metallurgy Monograph Series Geostatistics l South Africa Institute of Mining and Metallurgy Johannesburg South Africa Mandelbrot B B 1982 The Fractal Geometry of Nature W H Freeman Lon do
59. 44 13 8 0 50 15 9 0 56 9 10 0 62 11 0 69 0 75 Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 57 Chapter 5 Summary Statistics Cumulative Frequency Distribution The Cumulative Frequency Distribution window contains a graph of the cumulative frequency distribution for the Z variate If the data are transformed two graphs will appear with the distribution for the transformed data to the right of the distribution for the nontransformed data as below If the data are not transformed only the left hand graph will appear Transformations are performed in the Data Summary window If the data are normally distributed the curve will describe an S shape frequency distribution E G in the graph below transforming the data acts to normalize the distribution Cumulative Frequency Distribution Pb nl x NonTransformed Transformed 100 0 ws Cumulative Pct Cumulative Pct 0 0 0 06 0 46 0 85
60. 5 Grego 137 Chapter 12 Inverse Distance Weighting Inverse IDW and Normal NDW Distance Weighting 140 Table of Contents Chapter 13 Interpolation Output File Formats kro oda basia maet debel td d 142 Arclnfo or ArcView asc 143 Surfer amp grd Format sse 144 GSLib out Format 145 Chapter 14 Mapping The Mapping Window scnasena na 146 Map Contour Intervals sssssssssseeeee enne 150 BHO 152 Standard Deviations sss 153 torres LS 154 270 MADS circa cue ter eer acide dare ee p i v 155 Standard Deviations ssssssssssseeeenee 155 Sample Posting i iive dg aries 156 Transects 1 Maps eese 157 Standard Deviation ccceeccceseeeeeeeeeeeeeeeeeeeeeeeseaeeseaeeseneeees 157 Chapter 15 Bibliography etit ete raptos 158 Chapter 16 Glossary ornat n i ane 161 MINOX d H ANT 169 Chapter 2 Getting Started Chapter 1 Introduction GS is a geostatistical Analysis program that allows you to readily measure and il lustrate spatial relationships in geo referenced data GS analyzes spatial data for autocorrelation and then uses this information to make optimal statistically rigorous maps of the area sampled Th
61. 6333 9 499 467004 4 772509 10 e 79 708518 99 File Format A variety of text file types can be imported into GS including formats defined by the user Each type has its own manner for separating fields within data records for handling missing values for allowing header records and for specifying names of fields column titles within the file Predefined input format types include the follow ing examples of files appear in the next section GS format in which fields are separated by spaces free format or tabs miss ing values are indicated with the placeholder 99 the number of header records is automatically detected and column titles variate names appear on the 2 record separated by commas An example appears in the next section GeoEas format in which fields are separated with commas or spaces there are no missing value indicators the number of header records is specified on the 2 record of the file and column titles appear as individual records following this second record An example appears in the next section 45 Chapter 4 Importing Data from External Files Surfer XYZ format in which fields are separated by spaces free format miss ing values are indicated by blank fields and the first record in the file is a header record in which column titles variate names appear as fields separated by spaces Note that the Surfer XYZ format also allows fields to be separated by commas which shoul
62. As an example of the time savings possible 10 000 subsamples of a 160 000 point data set took 10 cpu minutes to produce essentially the same semivariogram model that otherwise took gt 8 cpu hours Each of the 10 000 subsampled points was compared to the 159 999 other points to produce the variogram 27 Chapter 2 Getting Started as opposed to when the full data set was sampled by comparing each of 160 000 points to 159 999 other points Number of subsamples specify the number of data records to use when subsampling large data sets IDW Interpolation Defaults Weighting Power 0 100 this value provides the initial default weighting power for inverse distance weighting IDW interpolation This value may be overridden from the Interpolate Window see Chapter 12 IDW and NDW for further information Smoothing Factor 20 this value provides the initial default smoothing factor for inverse distance weighting IDW interpolation This value may be overridden from the Interpolate Window see Chapter 12 IDW and NDW for further information Default to Normal Distance Weighting NDW sets the default IDW inter polation to Normal Distance Weighting NDW This value may be overrid den from the Interpolate Window see Chapter 12 IDW and NDW for further information Simulation Defaults Use different seed if this box is set each simulation will use a different random number seed by default See Chapter 10 Conditi
63. C Nonuniform intervals Define General Relative Variogram Pairwise Relative Variogram Standardized Variogram Madogram Rodogram Drift Correlogram Covariance Isotropic Variogram 0 273 0 205 8 0 137 E 8 0 068 0 000 0 0 28 0 56 0 840 Separation Distance h Anisotropic Variograms Model Expand Surface Isotropic Variogram Model Expand Active Lag Distance The Active Lag Distance specifies the range over which semivariance will be calcu lated The minimum distance for this field is the minimum distance between adjacent points in the data set while the maximum distance is the maximum distance be tween points Specifying a value too large or too small will assign respectively the largest or smallest possible values to this distance For example a 1200 m transect will have a maximum lag of 1200 m specifying an Active Lag of 300 m will limit the variogram to lag intervals less than or equal to 300 m along the entire 1200 m length of the transect The default active lag is specified in the Analyses tab of the User Preferences dialog 71 Chapter 6 Semivariance Analysis Overview window see Chapter 2 This is not likely to be the most appropriate active lag for your data but rather will provide a starting point Variograms typically decompose at large lag intervals because of decreasing numbers of couples per lag class as the maxi
64. For text files choose None Varies or Fixed Number Header records will be read into the Data Description field of the Data Worksheet Window Spreadsheet files are assumed to contain a single header row containing column names The Column Title Separator refers to whether column titles variate names appear in the second record of the file and if so how names are separated from one anoth er within the record For text files choose No Field Names Same as for Data Rec ords Quotes Brackets Comma Tab Space or Character When spreadsheets are imported columns titles appear in different cells of the first spreadsheet row OK Cancel Press OK to accept the settings shown and return to the Import Text File or Import 52 Chapter 4 Importing Data from External Files Spreadsheet dialog If the settings are different from the standard settings for the format originally defined the format will change to Custom with the new settings de fining the new Custom format Press Cancel to close without importing Viewing Files File View Window The file view window is used to display the contents of selected files It is available from windows in which input and output files are specified At the top of the window is the file name and size The contents of the window can be highlighted and copied to the Windows clipboard using the Edit Copy menu command but cannot be changed The example below was brought up from the View Output File command
65. GS User s Guide Version 10 GeoStatistics for the Environmental Sciences GAMMA DES IGN SOFTWARE Accessible Geostatistics for Everyday Science GS GeoStatistics for the Environmental Sciences Version 10 Gamma Design Software LLC Plainwell Michigan 49080 gammadesign com Copyright Copyright 1989 2015 Gamma Design Software LLC All Rights Reserved ISBN number 0 9707410 0 6 Information in this document is subject to change without notice and does not repre sent a commitment on the part of Gamma Design Software The software described is provided under a license agreement and may be used or copied only as specified in the agreement No part of this document may be reproduced in any manner whatsoever without the express written permission of Gamma Design Software Gamma Design Software P O Box 201 Plainwell Michigan 49080 U S A Citation The appropriate citation for this document is Robertson G P 2008 GS Geostatistics for the Environmental Sciences Gamma Design Software Plainwell Michigan USA Trademarks Microsoft and Windows are trademarks or registered trademarks of Microsoft Corpo ration Surfer is a registered trademark of Golden Software Inc ArcView and Arc Info are registered trademarks of ESRI Inc Other brands and their products are trademarks or registered trademarks of their respective holders and should be noted as such GS is a trademark of Gamma Design Software January
66. IDW files and the number of pairs used in the interpola tion for that x y location Missing values are denoted by whatever value is specified in the Preferences window Note that this format is different from the GS Input File format The following listing is for the first 6 coordinates for a standard GS krig output file A GS IDW Output file would look identical except that there would be no field for Estimated Standard Deviation in the data records GS Output Block Kriging Interpolation File v7 0 Set Field 54 Second Tier Dimensions 2 Interval source Calculated Interpolation interval x y 1 3333 1 3333 X coor m east range 0 00 80 00 Y coor m north range 0 00 80 00 Z est Pb range 0 151 0 813 Z sd range 0 0000 0 3655 Mean Z estimate sd 0 391 0 0186 Valid N 3721 Missing N 0 Missing Value Indicator 99 X Coordinate Y Coordinate Z Estimate EstStdDev n 0 00 0 00 0 431 0 3608 16 0 00 1 33 0 458 0 3486 16 0 00 2 67 0 462 0 3329 16 0 00 4 00 0 466 0 3178 16 0 00 5 33 0 470 0 3034 16 0 00 6 67 0 474 0 2900 16 142 Chapter 13 Interpolation Output File Formats ArcView and Arcinfo Format The ArcView Ascii asc format for Krig output files which is also the Arc Info format for Map input files contains a number of header records containing infor mation about the file followed by a string of z values for each row of the interpolated grid beginning in a particular corner Unlike GS format
67. Pb Isotropic Correlogram Correlogram 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90 Degra lt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 100 Chapter 7 Other Autocorrelation Measures Covariance Analysis Covariance in GS is computed as C h 1 N A X zizi n M n Mh where C h covariance for interval distance class N h total number of sample couples for the lag interval 2 measured sample value at point Zi measured sample value at point h m mean of all head values for lag h or 1 N X z and m mean of all tail values for lag h or 1 N h X Zin Cross covariance is computed in the same manner but z and zi represent two dif ferent variates Z and Z2 respectively The covariance graph appears in the Autocorrelation Window on the Covariance tab Press the Expand button to bring up the Covariance window 815 Pb Isotropic Covariance Covariance 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 80 Degre Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 101 Chapter 7 Other Autocorrelation Measures General
68. View input file that has fields for an x coordinate y coordinate and one z variate Note the three variate names in record 1 and the missing values in records 5 and 9 X data Y data Z data 4 5 11 9 0 42 2 7 29 4 0 45 1 6 32 6 0 08 4 1 0 65 0 6 64 0 14 2 4 71 8 0 32 Tei 34070542 Ge Tr L042 6 7 16 3 0 49 49 Chapter 4 Importing Data from External Files Text Input File Formats Surfer XYZ Format The standard Surfer input file format is comprised of header records and data rec ords a 50 Data records are space delimited XYZ type data This means that each data record contains at least 3 fields an x coordinate location a y coordinate loca tion and the value for at least one z variate measured at that x y location sin gle dimension transects will have only x coordinate and z variate data values Additional fields can hold other variates for that location e g sample ID other measured z variates A single header record precedes the data records and contains field variate names or column titles for the data record fields Names are space delimited so they must be single words e g mEast mNorth Nitrate in order that they be properly assigned to their columns You can allow names to be delimited by commas or other characters by changing this to a Custom Format in the File Im port Properties window e g meters East meters North Nitrate ug L Missing values are indicated by blank fields
69. Z Tab The Data Summary window provides standard descriptive statistics for the variates defined in the Data Worksheet window Information is provided for both the Z variate as below for the coordinate variates in a separate X Y Coordinates tab and when a covariate is being analyzed for the regression of Z vs the Covariate Z2 in a separate Regression tab For the Z variate it is also possible to specify a lognormal base e or square root transformation in order to better normalize the variate s distribution prior to geostatis tical analysis If you do transform the variate you may choose to have GS report the interpolated kriged values either in transformed form or backtransformed to the original measurement domain The backtransformation occurs after all analyses have been performed and it is not applied to autocorrelation results Also from the Data Summary window you can access a full window frequency distri bution a cumulative probability distribution or a normal probability distribution by clicking on the small frequency distribution image Data Summary Pb X Y Coordinates Transformation C Transformation C Scale to 0 1 Offset BackTrans formation Log Transform o C None C Standard Weighted C Square Root Transform a Summary Statistics Untransformed Transformed BackTransformed mean 0 382 1 1040 0 385 std d
70. ailable from these windows Model The Model command brings up a Model Dialog window within which you may change the variogram model The Model command is enabled only when the Show Model Variogram Option is selected Surface The Surface command brings up the Anisotropic Variogram Surface Map window The surface map is useful for visualizing anisotropic autocorrelation when present as described below Calculate The Calculate command causes the semivariogram to be calculated 74 Chapter 6 Semivariance Analysis Overview Define Irregular Lag Class Intervals Use this dialog window to specify individual lag classes that are not necessarily reg ular In the cells of the spreadsheet you can specify the upper bound of the distance interval classes desired Zero is always the lowest bound and the Active Lag Dis tance is always the upper bound regardless of values entered in this dialog In the example below note that classes are separated first by 3 distance units then by 5 10 and 20 units Lag Class Intervals Primary Variate Ur 9 xl Lag Class Upper Bound Clear Cancel OK Clear Clear the worksheet Import Import a text file containing the lag class interval bounds The default extension for lag class interval or step files is The format of the file to be imported is nu meric only records following a variable number of alphanumeric header records For example line 1 Optional header re
71. airs we can choose to mask rec ord 4 which has a value of 6 0 this can be confirmed in the Data Worksheet alt hough if the data are transformed the transformed value will not match the work sheet value This gives us a more reasonable variogram 1515 Pb Isotropic Variogram 0 0578 g o 2 0 0434 S 0 0289 E B 0 0145 0 0000 0 00 26 67 53 33 80 00 Separation Distance h Spherical model Co 0 01870 Co C 0 05590 Ao 80 00 RSS 1 215E 04 Isotropic 45 Degrees 90 Degre gt Scatter Right click to edit list print etc or click point for variance cloud Re examination of the variance cloud for lag class 7 below reveals that the highest y axis values are substantially lower than before 1 21 vs 167 4 and more im portantly all of the major outlier pairs are gone This was accomplished by removing a single data record from the analysis 109 Chapter 8 Variance Clouds and h Scattergrams iBixi Pb Variance Cloud Isotropic Lag Class 7 Variance 48 00 50 67 53 33 56 00 Separation Distance h Cloud Right click to edit list print etc or use mouse to identify points The right click menu and other commands work here as they do for the Variograms Window 110 Chapter 8 Variance Clouds and h Scattergrams Variance Cloud Pairs This read only window contains a listing of all pairs of points within a specific lag class including for each pair th
72. am modeling for the primary variate Z for the covariate Z2 and c for the cross variate Z x Z2 You will also want to check that the covariate is in fact correlated with the primary variate in the Data Summary Covariate window Once the three variograms are modeled you can choose the Cokrig tab in the In terpolation window Krig CoKrig simulate ow r Cokriging Type Simple Pin r Variogram Aniso Primary Variate c Secondary Variate e c Cross Variate c Use Relative Variogram r Discretization Point Kriging Block Kriging Cokriging Type GS provides three types of cokriging Simple Ordinary and Standardized Ordinary 138 Chapter 11 Kriging and Cokriging Simple cokriging places no constraints on the weights applied to the measured val ues during interpolation Ordinary cokriging sets the sum of weights applied to the primary variate to one and the sum of weights applied to the covariate to zero This limits the influence of the covariate relative to other cokriging types so may not be preferred Standardized ordinary cokriging recalculates the covariate to have the same mean as the primary variate and constrains all weights to sum to one This is often the preferred cokriging method and is the default cokriging type in GS Variogram Model Type Variogram models for isotropic and anisotropic variograms are defined and chosen using the Model command
73. an s I analysis 106 Mouse action 64 93 153 Multigrid refinements 28 NDW 28 141 Nearest neighbors 120 Neighborhood radius 121 Normal distance weighting NDW 28 141 Normal probability distribution graph 55 59 values 60 Nugget variance 79 80 87 163 Octant Search 121 Offset tolerance 73 Ordinary cokriging 140 Ordinary kriging 136 Ouput file formats 119 Outliers 108 Outline map 128 Output files ArcView format 144 Arc View format 120 GS format 120 143 GSLib format 120 146 148 interpolation 119 Surfer format 145 Surfer format 120 Pairwise relative variograms 104 Parameter files 16 166 Polygons definition 167 exclusive 119 126 128 how to create 119 173 Index inclusive 119 126 128 map 128 polygon definition window 126 vertices 126 Posting intervals 66 Postings See Coordinate postings Preferences analyses 26 anisotropy surface 27 autocorrelation Active lag default 27 autocorrelation defaults 27 autocorrelation lag intervals 27 data file import 25 decimal places 24 general 23 IDW smoothing factor 28 IDW vs NDW 28 IDW weighting power 28 import field assignments 25 import file type 25 import filename 25 interpolation output 28 missing value indicator 24 number of subsamples 28 simulation multigrid refinements 28 simulation number 28 simulation seed value 28 subsample data 27 variogram offset 27 Primary variate 138 Principal an
74. ange is limited to the number of decimal places specified for the given coordinate field in the Data Worksheet Win dow Changing the number of decimal places for a coordinate in the Data Worksheet Window changes the number of decimal places reported here Changing the range will change the Number of points value Note that interpolation will begin at the minimum X and Y values but may not reach the maximum values if the total distance e g the maximum X value less the mini mum X value is not evenly divisible by the distance interval For example interpo lation of an X Range of 0 105 with a distance interval of 10 will stop interpolating at X 100 prior to exceeding the maximum range of 105 Data Range This is the range covered by the actual data set these are read only values they cannot be changed by the user from this dialog window Distance Interval Specify the distance interval between locations within the interpolation range A dis tance interval of 2 0 over a range of 0 to 10 0 means that interpolations will be made at points 0 0 2 0 4 0 6 0 8 0 and 10 0 Changing the distance interval will change the value for number of points Number of Points For any given range to be interpolated the number of points will be the range divid ed by the distance interval plus 1 For a range of 0 to 10 0 with a distance interval of 2 0 the number of points will be 10 0 0 2 0 1 6 points at locations 0 0 2 0 4 0 6 0 8
75. ap Define brings up the Map Contour Intervals dialog window that allows you to set break points for individual intervals and colors for contour bands see Chap ter 12 for a description of the Contour Intervals dialog Map Legend Show legend displays the contour legend next to the map Continuous vs Stepped display legend as continuous scale with values next to break points e g between color bands or display legend as stepped format with values next to boxed colors Ceiling Contour lines project contour lines above the surface onto the ceiling of the plot 3 d maps only Color bands project color bands onto the ceiling of the plot 3 maps only Floor Contour lines project contour lines beneath the surface onto the floor of the plot 3 d maps only Color bands project color bands onto the floor of the plot 3 d maps only Grid Lines X axis place a vertical grid line along the back walls of the 3 d plot x axis 34 Chapter 2 Getting Started Y axis place a vertical grid line along the back wall of the 3 d plot y axis Z axis place horizontal grid lines along the back walls of 3 d plots Printing Copying and Exporting Graphs Graphs can be printed via the File Print menu If the active window contains a graph when the Print command is executed the graph on that window will be sent to the printer You may also right click on the graph to access a Print command A standard Windows P
76. at GS will conform substantially to the accompa nying written materials for a period of 1 year from the date of purchase provided that GS is used on computer hardware and with the operating system for which it was de signed 2 Gamma Design Software disclaims all other warranties either express or implied in cluding implied warranties of merchantability and fitness for a particular purpose This applies to both the software itself and accompanying written materials This lim ited warranty gives you specific legal rights you may have others that vary from state to state 3 Under no circumstances shall Gamma Design Software be liable for any damages whatsoever arising out of the use of or inability to use GS even if Gamma Design Software has been advised of the possibility of such damages Such damages in clude but are not limited to damages for loss of profits or revenue loss of use of the software loss of data the cost of recovering such software or data the cost of substi tute software or claims by third parties In no case shall Gamma Design Software be liable for more than the amount of the license fee as set forth below Some states do not allow the exclusion or limitation of liability for consequential or incidental damag es so this limitation may not apply to you User Remedies 1 Gamma Design Software s entire liability and your exclusive remedy shall be at Gamma Design Software s discretion either 1 refund of the
77. ata 38 42 Floor 34 150 Formulas in worksheets 39 Fractal analysis 107 Frequency distribution graph 55 56 values 57 Gaussian anisotropic model 90 Gaussian isotropic model 85 General relative variograms 102 GeoEas input file format 45 48 Geometric anisotropy 73 Geo referenced data 165 Graph settings axis scaling 31 axis titles amp labels 32 colors 29 contour details 33 footnote 30 general 29 legend 30 title 30 Graphs copying 35 data 19 exporting 35 printing 35 Grid lines 34 150 GS Input file format 45 GS Output files 143 GSLib output files 120 148 Header records 47 48 49 50 52 165 166 Help menu 21 Histogram bars 32 56 h Scattergrams 108 113 116 html files 18 35 IDW 141 interpolation defaults 28 output files 143 144 145 146 smoothing factor 28 141 142 weighting power 28 141 142 Importing data 18 default file type 25 default filename 25 file import dialog 44 import file command 37 spreadsheets 51 text files 45 Inclusive polygons 119 126 128 Indicator kriging 137 Input file format 45 ArcView XYZ 46 ArcView XYZ 49 Custom 46 Excel 51 GeoEas 45 48 GS 45 47 spreadsheet and database formats 51 Surfer XYZ 46 50 Insert 18 Insert rows or columns 39 Installation 6 171 Index Interpolate 165 Interpolation 117 block cokriging 140 block kriging 137 cokriging 117 138 conditional simulation 117 132
78. ay be nested within one another as in the example below However the vertices for each polygon must define a single closed polygon i e no segments of the polygon may cross another segment Also the first and last vertex specified must connect to one another You can check the shape of the poly gon while it is being defined with the Map command There are two types of polygons defined by the keyword Include and Exclude e In inclusive polygons the area within the polygon is interpolated e In exclusive polygons the area within the polygon is not interpolated The example below defines two polygons the first is a 6 sided area that is excluded from interpolation the second defines an inclusive 4 sided area rectangle inside the 6 sided area You can use the Map command to produce a picture of these pol ygons see below The first line in this example Polygon is unnecessary Each set of polygon vertices must be preceded by either Exclude or Include 2615 X Coordinate 1 mos Exclude zs 50 00 4 67 00 EE 67 00 6 55 00 7 55 00 Pts 50 00 9 Include 10 62 00 EET 65 00 12 65 00 ES E 62 00 14 15 Clear Clear the worksheet 125 Chapter 9 Interpolation Basics Import The Import command brings into the worksheet a text file containing vertex loca tions The text file can be formatted in a variety of ways with fields separated by either commas or spaces The d
79. be treated as missing values during the data build Range Range to use X direction 0 60 79 90 oef 000 Rea Y direction 1 50 79 90 1 4000 Re Z variate 0 06 1 25 ceW 25 mess Reset All Cancel Range to Use In these fields specify how to constrain the data in the Worksheet to a particular range In the example shown only those records for which the X direction field is within the range of 0 60 to 40 00 will be included in analyses even though there are records across the entire range of 0 60 79 90 in the worksheet Although Work sheet values are treated as missing during data builds they are not marked as miss ing in the Worksheet Reset and Reset All Reset Range to Use to the actual data range for a given coordinate or variate Data ranges can be set individually or with the Reset All command all at once OK Press OK to accept the ranges specified Note that for the filter to take effect you must check the filter box on the Worksheet window Press Cancel to exit the dialog without saving changes 42 Chapter 3 Working with Data Duplicate Values When worksheet data are rebuilt into data arrays GS checks each record against every other record to check that no duplicate coordinates are present If one or more records are found to be duplicates a warning screen will appear and you will be asked how to resolve the duplicate GS Duplicate Query Warning Data build was halted because reco
80. c and anisotropic variograms are chosen with the Model command in the Autocorrelation Analysis window Here in the Simulate win dow you can specify whether to use the isotropic or anisotropic model for the vario gram used in the kriging system Output Two types of output are available with conditional simulation either a the estimated Z value and its variance either estimation variance or standard deviation or b the probability that the estimated value for that location is greater than some threshold value t 131 Chapter 10 Conditional Simulation Anindividual Z estimate and its standard deviation is the mean and stand ard deviation of n simulations for a specific location Thus the number of simulations will affect both of these values Q Probability is the proportion of simulations for a specific location for which the estimated value is greater than t Thus this value will also be affected by the number of simulations Analysis tab Number of simulations You may choose any number of simulations 0 Keep in mind that choosing too few simulations will produce a map that is very rough although a large number of simulations may require substantial cpu time See later in this chapter for examples The default number of simulations is specified in the Preferences dialog Use different seed If this box is checked each simulation will use a different random number seed This will slow the analysis somewhat and make each si
81. cess is through a proxy server you may specify the server address and port number below See your local network administrator for the proper values Address examples proxy mycompany com or 292 191 22 3 Pot Back Use Proxy Server Check this box to connect to the internet using the proxy address and port specified This is useful if your network settings do not allow direct connection as is the case with some corporate and other servers Address Specify the proxy address to use Examples of valid address formats include proxy mycompany com and 192 191 22 33 Get the correct address from your net work administrator Port Specify a port to use for the proxy server Get the correct port number from your network administrator Chapter 2 Getting Started Activate over web Choose this tab to activate your copy of GS over the web rather than directly through the activation dialog This is useful if you cannot otherwise connect to the internet activation site Activate GS Advanced Options x 7 If you are experiencing firewall or other problems with direct activation you may also activate over Use Proxy Server the internet from any computer using Internet Explorer or another browser To activate using a browser 1 write down the installation ID below or copy to clipboard 2 open your web browser to http www internetactivation com press Get now below 3 enter your license number and the In
82. choose among three potential backtransformation choices None Standard or Weighted The standard backtransformation is simply the converse of the transformation scaled values are rescaled to the original range logn transformed values are raised to the natural exponent e and squared values are raised to the 0 5 square root Offset values are subtracted from the backtrans formed values The Weighted backtransformation is a complex backtransformation that more close ly approximates true population statistics than simple backtransformations See Haan 1977 and Krige 1981 for further details Backtransformations are applied only to final data These include statistics on the Data Summary screen mean standard deviation etc and all kriging results Indi vidual semivariance values are not backtransformed prior to display as noted by semivariogram axis labels Frequency Distribution Click on a frequency distribution image to view an enlarged version of the frequency distribution From the Frequency Distribution window you will also be able to view a normal probability distribution or a cumulative frequency distribution of the data see below Summary Statistics Descriptive statistics appear in the box noted Note that n refers to the number of active data items currently in the analysis 128 in the screen above n missing re fers to the number of worksheet records that were excluded from the analysis be cause they contained a mi
83. contain many variates but only one can be analyzed at a time thus only one column can contain the Z Variate data A Z Variate Column must be defined prior to spatial analysis To specify a column click on the top row of the worksheet Z2 Variate Data Z2 or Covariate The Z2 Variate or Covariate is a second Z variate that covaries with the primary Z variate It is used in cokriging 168 Index 1 d transects 158 2 d maps 33 147 156 3 d maps 33 147 153 ceiling 34 floor 34 grid lines 34 map proportion 33 Standard deviations 154 Ao 79 80 82 83 84 85 167 Aj 86 87 89 90 91 168 Activation 7 activate over the web 10 activation code 7 8 activation window 8 advanced options 9 deactivation 7 11 evaluation mode 8 installation ID 10 license number 8 proxy server 9 serial number 7 Serial number 8 unlocking code 10 Activation server 22 Active lag distance 27 71 Adjacency matrix 106 Anisotropy axis orientation 73 92 94 semivariance surface 73 74 94 Semivariance surface 92 surface map 27 variogram map 92 94 variogram models 86 Appending data 53 ArcView input file format 46 map input files 148 output file format 120 output files 144 Assign field 40 Autocorrelation active lag default 27 autocorrelation window 71 correlograms 100 covariance analysis 101 defaults 27 definition 162 drift 99 fractal analysis 107 general relative variograms 102 madogra
84. cord 1 line 2 Optional header record 2 line 3 2 0 line 4 4 0 line 5 8 0 line 6 12 0 line 7 30 0 line 8 100 0 75 Chapter 6 Semivariance Analysis Overview This file describes 8 lag classes 0 to 2 0 2 0 to 4 0 4 0 to 8 0 8 0 to 12 0 12 0 to 30 0 30 0 to 100 0 100 0 to maximum lag distance You can adjust the active lag to be any value up to and including the maximum dis tance separating points in the input file i e the maximum lag distance Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 76 Chapter 6 Semivariance Analysis Overview Variograms Window The Variograms window presents a full window variogram that can be edited and printed Different tabs hold variograms for the different anisotropic directions Addi tionally the semivariance values that were used to produce the variogram can be listed and Variance Cloud Analysis can be performed Variance Clouds
85. covariate values outnumber primary values Please ensure that column assignments are corect Press ok to continue data build 1 Cancel Help Missing Values Data in the Worksheet that are marked as Missing are ignored during analyses Permanent missing values appear as blank cells and temporary missing values ap pear in red You can use the right mouse button to make cells temporarily missing and vice versa When importing or exporting files special placeholders values or symbols can be used to indicate missing values in the incoming or outgoing data file These place holders are specified by the user in the Preferences window or during file imports by a value or symbol specified in the File Import Properties window In GS the default missing value indicator is the numeric value 99 0 but this can be changed in the User Preferences window Chapter 2 Missing values appear in output files when a value cannot be interpolated because the location appears in an exclusive polygon or because numerical limitations disal low its computation such as when a variogram model is inappropriately used during kriging 41 Chapter 3 Working with Data Data Filter Dialog The data within a worksheet can be collectively filtered or bounded using the Filter command on the Data Worksheet window With this command all records are scanned and if a record falls outside of the specified Range to Use the variate out side of its range will
86. cross validation and jackknife graph represents a location in the input data set for which an actual and estimated value are available Information about individual points is provided at the bottom of the screen points are displayed by placing the cursor on them In the case above the cursor was placed on the point representing record 100 as noted at the bottom of the window By right clicking on the graph you can list the data for all points see below The regression coefficient described at the bottom of the graph represents a meas ure of the goodness of fit for the least squares model describing the linear regres sion equation A perfect 1 1 fit would have a regression coefficient slope of 1 00 and the best fit line the solid line in the graph above would coincide with the dotted 45 degree line on the graph The standard error SE 0 162 above refers to the 128 Chapter 9 Interpolation Basics standard error of the regression coefficient the r2 value is the proportion of variation explained by the best fit line in this case 37 996 it is the square of the correlation coefficient and the y intercept of the best fit line is also provided The SE Prediction term is defined as SD x 1 r where SD standard deviation of the actual data the data graphed on the y axis If you have chosen to transform the input data without a backtransformation see the Data Summary window then the Estimated Z values will appear very diff
87. d be specified separately as described below Note that this format is not the same as the Surfer Grid file format that can be used for Krig output files or Map input files An example appears in the next section ArcView XYZ format in which fields are separated with commas missing val ues are indicated by placeholder commas there is a single header record and within the header record variate names are separated by quotes and commas An example appears in the next section Q Custom in which any of these format specifications can be changed or custom ized as specified in File Import Properties as described in the next section Properties The Properties Command brings up a File Import Properties dialog window de scribed below within which you can specify the rules for GS file imports Change Column Assignments The Change command brings up a Field or Column Assignment window from which you can assign variates e g X coordinate to columns or fields in the data file see below Columns can also be assigned later from the Data Worksheet window Assign Fields Columns x Column Assignment Assign To Variate Column IV Sample ID M X Coordinate 2 M Y Coordinate 5 M Z Primary Variate 4 n 22 Covariate 4 E l Drift B 46 Chapter 4 Importing Data from External Files Text Input File Formats GS Format The standard GS input file format is comprised of header records and data recor
88. ds Q Data records are space delimited or tab delimited XYZ type data This means that each data record contains at least 3 fields an x coordinate location a y coordinate location and the value for at least one z variate measured at that x y location single dimension transects will have only x coordinate and z variate da ta values Additional fields can hold a sample ID value and multiple z variates for a particular x y location Header records precede the data records and contain whatever text information about the file that the user feels is useful There can be any number of header records for this format GS determines the number of header records automati cally which means that data records start with the first all numeric record The last header record can contain column titles variate names separated by commas Q Missing values are denoted by the number 99 Any of these parameters field delimiters number of header records missing value indicators etc can be changed to a custom format from the Import Data File window The following listing is the first 11 records of a standard GS input file that has fields for sample ID x coordinate y coordinate and two z variates Note the variate names in the second record and two missing values in the last column File Demo2 d dat sample m east m north Pb Al 1 4 5 Ereg 0 42 0 42 2 2 7 29 4 0 6 0 45 3 1 6 32 6 0 6 0 08 4 4 1 44 5 0 43 99 00 5 0 6 64 04 5
89. ds work here as they do for the Variograms Window 98 Chapter 7 Other Autocorrelation Measures Drift Drift also called trend is calculated as F h 1 N A E zi Zin where F h drift for interval distance class h 2 measured sample value at point Zin measured sample value at point h and N h total number of sample couples for the lag interval h Drift graphs both isotropic and anisotropic appear in the Autocorrelation Window on the Drift tab Press the Expand button on this tab to bring up the Drift window 015 Pb Isotropic Drift 0 161 0 080 0 000 E Doo 0 080 zu otop 0 161 0 00 26 67 53 33 80 00 Separation Distance h isotropic 0 Deoress 45 Degrees neve IP Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 99 Chapter 7 Other Autocorrelation Measures Correlograms Correlograms are calculated using the formula p h C h c where p h correlation for interval distance class 6 5 Standard deviation of all head values 2 for lag h and 6 4 standard deviation of all tail values Z for lag h Correlograms both isotropic and anisotropic appear in the Autocorrelation Window on the Correlogram tab Press the Expand button on this tab to bring up the Corre logram window 5 5
90. e squared average of tail and head values yPR A 1 2N A E zi Zin o 5 zi Zin where yPR h pairwise relative semivariance for interval class N h total number of sample couples for the lag interval h z measured sample value at point and Zi measured sample value at point h Relative variograms can be calculated only for data sets for which all Z values are positive otherwise the denominator above could equal zero If the minimum Z val ue in the active data is 0 then the relative variogram will not be drawn To avoid this problem you can first scale or otherwise transform the data in the Data Sum mary Window Pairwise relative variograms both isotropic and anisotropic appear in the Autocor relation Window on the Pairwise Relative Variogram tab Pairwise relative vario grams are not available if the minimum Z value is less than zero Press the Expand button on this tab to bring up the Pairwise Relative Variograms window inixi Pb Isotropic Pairwise Relative Pairwise Relative Semivariance 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90 gt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 104 Chapter 7 Other Autocorrelation Measures Moran s 1 Analysis The Moran s statistic is a co
91. e Data Change Decimals menu commana Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 111 Chapter 8 Variance Clouds and h Scattergrams h Scattergrams In an h Scattergram each head value 2 is plotted against each tail value zj for a giv en lag class h The formula to calculate this difference for any given pair of points at locations i and j is Dj 2 7 where D difference for pair ij 2 measured sample value at point and zj measured sample value at point j Note that an h Scattergram is specific to both direction isotropic or a specific aniso tropic direction and to a particular lag class In the variogram below displayed ear lier the cursor is on the point representing lag class 7 of the isotropic variogram which looks odd Variograms Pb B x Pb Isotropic Variogram 2 12 2 1 59 3 106 ue E d 053 0 00 0 00 26 67 53 33 80 00 Separation Distance h Exponential model Co 0 31800 Co C 2 64600 Ao 67 RSS 0 262 Isotropic 45Degrees 90Degre lt gt Scatter Lag Class 7 995 pairs click for variance cloud Clicking on this variogram point or pressing the Scatter button brings up the h Scattergram for lag class 7 below and it becomes apparent t
92. e Weighting Krig Simulate Weighting Method Inverse Distance IDW C Normal Distance NDW Weighting Power Value 0 100 E Smoothing Factor Value gt 0 H Reset Inverse vs Normal Distance Weighting Choose either inverse distance weighting or normal distance weighting Inverse weighting applies stronger weights to nearby points than does Normal Distance Weighting Weighting Power The weighting power defines the rate at which weights fall off with distance between the interpolated and sample locations A value of 1 5 is typical Smoothing Factor The smoothing factor s reduces the likelihood that any one sample value will overly influence an estimated value for a given interpolation location Reset Restore default values to the IDW method 141 Chapter 13 Interpolation Output File Formats Chapter 13 Interpolation Output File Formats GS Format Output Files The GS format for Krig krg IDW and Conditional Simulation output files which is also the GS format for Map input files contains a number of header records con taining information about the file followed by XYZ style records for each interpolated points Each data record contains fields for an x coordinate value a y coordinate value except 1 dimensional transects do not contain a value for the y coordinate an estimated z value for that x y location an estimation standard deviation for the estimated z value except
93. e analysis Z x Z2 rather than semivari ance analysis Z or Z2 is performed Cross semivariance analysis must be per formed prior to cokriging For a description of the commands and options provided in this window please see the description of the Semivariance Analysis Window above Cross Autocorrelation Analysis E E E x Active Lag Distance 8200 2 Anisotropic Axis Orientation Cucine Ext Lag Class Distance Interval a Principal Axis degrees N o cere are ERES f Uniform interval 0024 Offset tolerance degrees 22 50 Pa NEN C Nonuniform intervals Define Cross Covariance General Relative Cross Variogram r centran m Cross Variogram Standardized Cross Variogram Madogram Rodogram Drift Cross Correlogram e B 0 425 0 283 Semivariance 0 142 0 000 0 00 21 53 43 05 84 58 86 10 ient Separation Distance h isotropic Variogram Model Expand Anisotropic Variograms Model Expand Surface Commands in the Cross Autocorrelation window are the same as in the Autocorrela tion window earlier in this chapter 95 Chapter 7 Other Autocorrelation Measures Chapter 7 Other Autocorrelation Measures Standardized Variograms In standardized variogram analysis the variogram is computed as a proportion of sample variance y h 1 2N A Z Zan s where y h Semivariance for interval distance class h 2 measured sample value at point Zi
94. e default rotation angle and scale Mouse Location The current cursor location when on the map surface Units are map units Graph Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu 152 Chapter 14 Mapping Map Image 3 d Standard Deviations A map of standard deviations can be produced for interpolation files that contain standard deviation or estimation variance values Krig or Conditional Simulation interpolations that are saved in GS format Use the Draw command from the Map ping window Map Image Pb SD 1 151 xl Pb SD Mouse Action 0 151 Off 0 146 0 141 Reset 0 130 0 125 Mouse Location 0 119 X 76 7 0 114 33 9 0 109 7 0 103 Z 0 097 Commands in this Window are the same as for earlier graphs 153 Chapter 14 Mapping Map Image 3 d Rotation Three dimensional map images can be rotated to any viewing angle To rotate choose Rotate on the Mouse Action panel and hold down the left mouse button while moving the mouse over the graph The cursor will be replaced with a 3 d box as below of the viewing angle Release the mouse and the map will be drawn Map Image Pb ni xj Mouse Action Rotate Pb Reset 0 733 0 693 0 653 Mouse Location Map Image Pb ni xj Mouse Action Rotate Pb Reset Mouse Location 154 Cha
95. e for each X and Y Coordinate location that is kriged the interpolation or Z estimate the standard deviation of the Z estimate and the number of neighbors that were used to make the estimate See detailed example in Chapter 11 Surfer Grid format grd in this format a short header area defines information needed for mapping and the data is written as a continuous stream of Z estimates beginning from a specific corner of the interpola tion grid The standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format This format is compatible with Golden Software s Surfer mapping program Note that this format is not the same as the Surfer XYZ Input file format See detailed example in Chapter 11 ArcView Format asc this is similar to the Surfer format but the header area is formatted differently and the Z estimates are written in a pattern that begins from a different corner of the interpolation grid The standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format Also for this format the x and y interpolation intervals must be the same you can set them to be the same from the Interpolation Grid dialog window This format is compatible with ESRI s Arc Info Geographic Information System See detailed example in Chapter 11 GSLib Format out out this format is similar to the GeoEas input format A long f
96. e maps can be created in GS or in other mapping programs or geographic information systems When do need geostatistics Geostatistics is useful when you need to make accurate statistically rigorous maps created from incomplete data which means whenever you make a map for a prop erty that cannot be exhaustively sampled Whether you are mapping oil deposits or plankton distributions geostatistics allows you greater confidence in the interpolated values for the locations not actually sampled Statistics Provided by GS GS provides spatial autocorrelation analysis Semivariance analysis produces variograms and different types of variogram models including isotropic and anisotropic variograms Anisotropic variogram maps make it easy to recognize anisotropy h Scattergrams and Variance clouds provide an easy way to recognize data outliers and Many other types of autocorrelation measures including Moran s 1 fractals cor relograms covariograms madograms rodograms drift standardized vario grams and general and pairwise relative variograms GS provides fast interpolation Various types of kriging provide optimal interpolation of a discrete point or an area around a sample point location Conditional simulation provides probability based interpolations and estimation error Chapter 2 Getting Started Cokriging provides optimal interpolation when you have only a few samples for the primary variate but many samples fo
97. e quartile plot below Block kriging following variography resulted in the adjacent map 8000 an t QU 6000 t 100 2000 4000 8600 LT a Soil carbon easier to measure than Uranium was sampled at the same locations as Uranium and additionally at another 60 locations as noted in the quartile map below left Regression of carbon against plutonium showed that the variates were highly correlated right suggesting that cokriging might improve the map of plutonium 020 2 2 000 1000 4008 0 09 om ma T Using carbon as a covariate to produce a cokriged map of plutonium results in the below right map plotted next to the original kriged map Note the substantial im provement in the definition of contour isoline differences especially in the upper right quadrant of the map where the uranium was sampled most sparsely 137 Chapter 11 Kriging and Cokriging we of oo n ac LT 40 wo The kriging estimate is based not only on distance to nearby sample locations for Z and the variogram for Z but also distance to nearby sample locations for Z2 the variogram for Z2 and the cross variogram for Z x Z2 This can provide a more ro bust estimate of Z at unsampled locations if Z and Z2 are sufficiently correlated Prior to cokriging you must a define a covariate in the Data Worksheet Field As signment dialog b perform semivariance analysis including variogr
98. e success of a transformation can be judged by observing its frequency distribution before and after transformation Values may be backtransformed prior to reporting results Regular Lag Interval Classes The Lag Class Distance Interval defines how pairs of points will be grouped into lag classes Each point in a variogram or autocorrelogram represents the average sem ivariance or Moran s I for a single lag class which is a group of pairs separated by a certain Lag Class Distance Interval sometimes called a step size This interval can either be calculated by GS in which case it will be regularly distributed across the active lag distance or it can be manually set by the user Variogram Model Parameters Model parameters for isotropic variograms include terms for nugget variance Co the combined nugget plus structural variance Co C also called the model sill and the range parameter Ao or in the case of anisotropic variograms A a function of A and A The range parameter may be different from the effective range which should be used to compare ranges among models 167 Chapter 16 Glossary What is a valid record A valid record is any record that contains non missing values for the coordinate loca tions both an X Coordinate value and a Y Coordinate value for 2 dimensional do mains AND a non missing value for the Z Variate Missing values appear as blank cells OR as red colored text use the right mouse button to turn cells
99. e variance separation distance and the identity da ta record number of each member of the pair These pairs are graphed in the Vari ance Cloud window Note that in the example below sorted by variance with pairs of highest variance listed first record 4 shows up as a member of the each one of the 14 high variance pairs This confirms record 4 as an outlier which was determined in the variance cloud graph above Variance Cloud Pairs Pb 1 0 06 13 0000 49 12 167 44 Distance jh to 4 13 00 87 0 1800 49 99 164 35 H 13 00 97 0 2000 52 18 163 84 13 00 88 0 2000 48 14 163 84 48 0 21 13 0000 50 18 163 58 4 13 00 67 0 2300 48 90 163 07 13 00 76 0 2300 54 57 163 07 4 13 00 95 0 2500 55 84 162 56 4 13 00 96 0 3000 52 77 161 29 13 00 89 0 3200 50 08 160 78 4 13 00 82 0 4900 50 05 156 50 13 00 83 0 5200 51 56 155 75 4 13 00 98 0 7100 53 79 151 04 4 13 00 92 0 9400 52 28 145 44 59 0 15 115 1 2500 49 84 1 21 94 0 18 115 1 2500 52 01 1 14 102 0 19 115 1 2500 53 34 1 12 35 0 21 115 1 2500 53 40 1 08 42 0 23 115 1 2500 55 73 1 04 24 0 24 115 1 2500 50 61 1 02 29 0 24 115 1 2500 55 73 1 02 Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use th
100. ecords Records at the top of a data file that precede the data records and that contain in formation about the data records Interpolate An interpolate is an estimated value for a location in a domain based on values of nearby measured locations In GS interpolation is performed by kriging or by in verse distance weighting methods Maps are based on interpolations at grid points across the domain Kriging An interpolation method based on regionalized variable theory that provides an op timal interpolation estimate for a given coordinate location Lag Class Distance Interval Each point on a variogram corresponds to the average semivariance for all values in the spatial domain that are separated by a given distance interval h This interval also called a lag distance class is a range whose width is specified by the user in the Semivariance Analysis window A corresponding definition is also relevant to Moran s I Fractal Cross Semivariance and Madogram Analyses 164 Chapter 16 Glossary Missing Value A value not present in a record A data record can contain fields for coordinates e g X Y and for multiple Z variates If any one of the fields used for an analysis is miss ing the record is ignored during analyses i e when the active data set is built In the GS Worksheet a value is considered missing if the cell is blank a permanent miss ing value or if the cell contents appear as red italicized text a temporarily miss
101. efault file name extension for polygon interpolation outline files is int Map Produces an outline map of each polygon within the larger interpolation grid area Exclusive polygons appear in red inclusive in blue Drawing a map is a useful way to test your polygon coordinates See the example in the next section Other Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu commana Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 126 Chapter 9 Interpolation Basics Polygon Outline Map This window contains an outline map of the polygons used to include and exclude areas from interpolation It is accessed from the Define Polygon Outlines window which is part of Interpolation analysis The overall area is the interpolation area specified in the Interpolation window Poly gons are defined in the Define Polygon Outlines worksheet Exclusive polygons ap pear in red inclusive in blue Polygon Outline Map Pb 1 nl 88 00 64 00 2 T 2 40 00 19 16 00 8 00
102. emivariogram reaches an asymptote The formula used for this model is Y h Co C 1 5 h Ao 0 5 h Ag for h lt Ao y h Co C for h gt Ao where y h semivariance for interval distance class h h the lag distance interval nugget variance gt 0 structural variance 2 Co and A range parameter In the case of the spherical model the effective range A Spherical Model 0 254 0 191 Semivariance e N J 8 0 000 0 0 20 5 41 0 61 5 82 1 Separation Distance h 82 Chapter 6 Semivariance Analysis Overview Exponential Isotropic Model The exponential isotropic model is similar to the spherical in that it approaches the sill gradually but different from the spherical in the rate at which the sill is ap proached and in the fact that the model and the sill never actually converge The formula used for this model is y h Co exp h Ao where Semivariance y h semivariance for interval distance class h h lag interval C nugget variance gt 0 C structural variance gt Co and Ao range parameter In the case of the exponential model the effective range A 3A which is the distance at which the sill C Co is within 596 of the asymptote the sill never meets the asymptote in the exponential or Gaussian models Exponential Model 0 254 0 191 0 0 127 0 064 0 000 0 0 20 5 41 0 61 5 82 1 Separation Distance h
103. erage semivariance for those points and the number of pairs of points upon which the average distance and semivariance are based This is a read only worksheet x La Avera Cass Distance Semwaranc 1 5 78 0 0093 218 2 1273 0 0101 656 3 20 74 0 0137 952 4 28 68 0 0144 1142 5 37 01 0 0168 1172 6 45 16 0 0179 1123 7 53 26 0 0093 940 8 61 36 00191 732 9 69 41 0 0144 510 10 77 40 00116 211 Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 78 Chapter 6 Semivariance Analysis Overview Isotropic Variogram Models The variogram is a graph of semivariance vs separation distance Where autocor relation is present semivariance is lower at smaller separation distances autocorre lation is greater This typically yields a curve such as that described below which can be modeled using three terms a nugget variance a sill and a range GS provides four types of isotropic models each of
104. erent from Actual Z values regardless of the integrity of the interpolation system 129 Chapter 9 Interpolation Basics Cross Validation and Jackknife Values In cross validation analysis each measured point in a spatial domain is individually removed from the domain and its value estimated via kriging as though it were never there In Jackknife analysis estimates are compared against measured values for a set of locations different from those used as input data Results can be graphed see above as well as listed in this read only worksheet table Note that Estimated Z values may or may not be backtransformed depending on settings in the Data Summary worksheet If you have chosen to transform the input data without backtransforming then the Estimated Z values will appear very different from Actual Z values regardless of the integrity of the interpolation system x Record Actual Z 1 0 420 2 0 600 3 0 600 4 0 430 5 0 510 6 0 340 7 0 370 8 0 610 9 0 460 10 0 440 11 0 380 12 0 470 13 0 440 14 0 370 15 0 610 16 0 560 0 440 Table The record number refers to the actual record in the Data Worksheet For each rec ord successfully kriged the actual Z value is presented in the middle column and the estimated Z value is provided to its right Other Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You
105. ete functions are also available from the right click menu dum Edit Ctri4E Cut Ctrl C Paste Coley Delete Del o Export Print Ctrl P List values User Preferences General Tab The Preferences dialog allows you to set user default values for some GS behav iors There are three categories available General settings as described here settings for Data File Import and settings for Analyses x General Data File Import Analyses Reset Missing value indicator 99 V Show tips i Put Z Name in Window Title Window background color WM Show all warnings Default graph background r Places past decimal to report for Covariate Z2 Transformed Y Coordinate Automatic C User defined 2 Automatic C User defined 2H Z Variate Nontransformed Z Variate Transformed Automatic C User defined 2 Automatic C User defined 3H Covariate Z2 Nontransformed Covariate Z2 Transformed Automatic C User defined 2 Automatic C User defined 2 External Drift Automatic User defined 234 Save Exit Reset The Reset command returns all user default values on this tab to original default values To reset all values on all tabs use the Global Reset command at the bot 23 Chapter 2 Getting Started tom of the window Missing Value Indicator Specify the value used by GS on output files and when impo
106. eters Proportion C Co C this statistic provides a measure of the proportion of sample variance Co C that is explained by spatially structured variance C This value will be 1 0 for a variogram with no nugget variance where the curve passes through the origin conversely it will be 0 where there is no spatially dependent variation at the range specified i e where there is a pure nugget ef fect Statistics AutoFit Statistics for the Autofit model the model most recently calculated by GS appear in this box In this way you can compare your changes to model terms against that calculated automatically Autofit Automatically refit the model using as starting conditions the parameters in this dia log window Model fitting in GS is somewhat dependent on starting conditions as sumed model parameters prior to iterations Sometimes you can fit a better model by hand in which case Refitting will further refine parameters to minimize RSS To return to the original model parameters you may need to exit this Model definition window and recalculate the variogram OK Cancel Press OK to close the dialog window and apply any changes made to individual models Press Cancel to exit the dialog window without applying changes Spherical Anisotropic Model The spherical anisotropic model is a modified quadratic function in which at some distance A along the major axis and A along the minor axis pairs of points are no longer autocor
107. eviation 0 206 0 5470 0 227 sample variance 0 04237 0 2992 0 05172 minmum value 0 06 2 8 Click on graph to maximum value 125 0 2 enlarge n n missing or excluded 128 4 128 frequency distribution Z 1 31 0 21 0 29 0 21 Ex 2 74 0 42 0 05 0 42 Transformation It is often helpful to apply a lognormal or a square root transformation to a Z variate in order to normalize for skewed frequency distributions It can also be useful to scale data to a range of 0 1 if the values are extremely large The transformation 54 Chapter 5 Summary Statistics specified is applied to every Z value in the data set prior to geostatistical analysis the values in the data worksheet are not transformed View the effectiveness of the transformation by viewing the Frequency Distribution or a probability distribution and the values for skewness and kurtosis in the data summary Offset If your z variates span the range of 1 to gt 1 e g 0 3 to 20 1 and you decide to ap ply a lognormal or square root transform you should make all values 1 prior to transformation by adding an offset value such as 1 e g In z 1 This is because of the discontinuous nature of the lognormal transformation across the 1 to gt 1 range Backtransformation When a transformation is chosen after analysis of the transformed data the output data are customarily but not necessarily back transformed to the original data do main when reported You may
108. ext information desired can be entered in this field When importing text files the header records in the file the records that appear prior to the data records are automatically read into this box If specified in the text file import window these records can also contain variate names that appear as data column titles The first line of the Data Description becomes the default graph and worksheet title You can use this box for storing comments about the parameter file or analysis Data Records The first row of the data worksheet holds the field or column numbers You can click on a cell in this row to sort the contents of the column in ascending or descending order each time you click the order is alternated All row contents are sorted when you sort a particular field or column The second row of the data worksheet specifies the Field or Variate Assignments i e which field or column contains the X Coordinate Data Y Coordinate Data Z Variate Data or Sample ID Data These assignments can be changed by clicking within the top row which will bring up a Field Assignment Dialog window The third row of the data worksheet specifies the user supplied Field or Variate Names for the various data fields or columns To enter or edit names click on the 38 Chapter 3 Working with Data cell to be edited When data is imported from a text or external worksheet file vari ate names can be read from the header records The data a
109. fference dk 0 06 E 13 0000 49 12 12 94 13 00 0 1800 49 99 12 82 13 00 0 2000 52 18 12 80 13 00 0 2000 48 14 12 80 0 21 13 0000 50 18 12 79 13 00 0 2300 48 90 12 77 13 00 0 2300 12 77 13 00 0 2500 12 75 13 00 0 3000 12 70 13 00 0 3200 12 68 13 00 0 4900 12 51 13 00 0 5200 12 48 13 00 0 7100 12 29 13 00 0 9400 12 06 0 15 1 2500 1 10 0 18 1 2500 1 07 0 19 1 2500 1 06 0 21 1 2500 1 04 0 23 1 2500 1 02 0 24 5 1 2500 1 01 0 24 1 2500 5 1 01 D aaaea sb on n n n n n 2166 N nH amp in c in n n w prt 4 4 4 4 4 4 4 on wo 4 ocn m N 4 D Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 115 Chapter 9 Interpolation Basics Chapter 9 Interpolation Basics Interpolation is the estimation of values in an area for points not actually sampled There are many different interpolation techniques ranging from simple linear tech niques
110. files that have been saved in the standard GS format Map Input File File Format ITADemo2d Cokrig krg es Grid krg M Draw Exit View Map Grid Variate to Map X direction 0 0 80 0 v 2 values Y direction 00 800 m Std devi Z values 111 E Z SD values 0 00 1 15 N N missing 3721 0 UP Map Legend Map Type V Show legend s 9 9 Continuous Stepped Map Surface Map Contour Levels Map Ceiling Contour lines Solid pedesta Number 15224 Dele Contour lines Color band M Color bands V Wireframe Axis Grid Lines Map Floor smoothing 2 Yaa 2 Contour ines 7 Color band Map Input File e Select allows you to choose the file with the data to be mapped The de fault file extension will correspond to the selected file format e g krg blk and pun for GS format although a file with any extension can be selected e View view the selected file in the View File window e Format specify the format to use to read the input file Files with a krg blk or pun extension are assumed to be in GS format The format specified in this field will override any assumed format 146 Chapter 14 Mapping GS Krig format krg in this format a header area defines the interpo lation grid variate names and other information about the file needed to initiate mapping later and the data records includ
111. for IDW interpolation block size is irrelevant and is ignored during analysis Clear Clears the worksheet 123 Chapter 9 Interpolation Basics Import The Import command brings into the worksheet a file containing interpolate loca tions See Chapter 4 Importing Data from External Files for instructions on import ing Other Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu commana Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 124 Chapter 9 Interpolation Basics Polygon Outlines Interpolation Masks Irregular shapes can be interpolated or excluded from interpolation by defining inclu sive or exclusive polygons prior to interpolating In this window you can define these polygons by entering coordinates of polygon vertices i e x y points that outline the polygon Polygons must be closed thus they must have at least 3 vertices 3 vertices de scribe a triangle You may specify as many vertices per polygon as you like up to several million and polygons m
112. geometric anisotropy i e anisotropy which is expressed as vario grams with different ranges in different directions The Principal Anisotropic Axis the Major Axis of the anisotropic model is the direction with the longest range i e the direction of major spatial continuity The best way to evaluate anisotropy is to view the Anisotropic Semivariance Surface Variogram Map and use the Azimuth function to define and then set the Principal Anisotropic Axis to the direction aligned with the lowest semivariance values the direction of maximum spatial continuity or major axis of the anisotropic variogram model The map is accessed by pressing the Surface command at the bottom of the Semivariance Analysis window Principal Axis degrees N The Principal Axis is the direction of maximum spatial continuity or base axis from which the offset angles for anisotropic analyses are calculated Offset angles are 0 45 90 and 135 clockwise from the base axis points aligned sufficiently close to one or another of these angles see Offset Tolerance below are included in the ani sotropic analysis for that angle The axis orientation should correspond to the axis of maximum spatial continuity i e the major anisotropic axis The default axis is 0 from the north south y axis Choose the appropriate axis value by using the Surface command to bring up the Anisotropic Variogram Surface window Offset Tolerance degrees In anisotropic analyse
113. gle computer You may use GS on a network or file server ONLY if ac cess is limited to one user at a time and you have the original copy of the documenta tion and program media GS requires activation over the internet You may transfer the license from one computer to another by deactivating the license on the computer on which it is cur rently installed and reactivating the license on another computer You do not have the right to activate or otherwise use GS on more than one computer hard disk drive or file server at a time 2 is owned by Gamma Design Software and is protected by United States copy right laws and international treaty provisions GiS must be treated like any other copyrighted material although you may either 1 transfer GS to a single hard disk drive so long as you keep the original copy for the purpose of backup or 2 make one copy of GS for backup purposes The written material accompanying GS may not 12 Chapter 2 Getting Started be copied 3 GS4 may not be rented or leased but may be permanently transferred if you keep no copies of any version of GS and the recipient agrees to the terms of this agreement 4 You may not decompile disassemble or reverse engineer GS 5 Gamma Design retains all rights not granted expressly herein Nothing in this Agree ment constitutes a waiver of Gamma Design s rights under any federal or state law Limited Warranty 1 Gamma Design Software warrants th
114. hat a number of pairs are very different from the others Placing the cursor over each point reveals that all of the points farthest from the 45 degree line contain record 4 as a member of the pair the cursor below is over the point represented by records 4 and 92 with a sepa ration distance of 52 28 112 Chapter 8 Variance Clouds and h Scattergrams ipi xd Pb h Scattergram Isotropic Lag Class 7 Records 4 and 92 Click for details Head Value o 8 0 00 433 8 67 13 00 Tail Value Cloud Scatter Pair 67 Records 4 and 92 separation distance 52 28 Clicking on this h Scattergram point brings up the Sample Details window which gives us the option to temporarily mask remove from the active data set one of the data records for this pair Sample Details Head Record 4 Z value 13 000 Mask Tail Record 92 Z value 0 940 Mask Separation Distance h 52 28 Distance 01 12 060 Since record 4 is a member of all of these outlier pairs we can choose to mask rec ord 4 which has a value of 6 0 this can be confirmed in the Data Worksheet alt hough if the data are transformed the transformed value will not match the work sheet value This gives us a more reasonable variogram 113 Chapter 8 Variance Clouds and h Scattergrams igi xd Pb Isotropic Variogram 0 0578 0 0434 0 0289 Semivariance 0 0145 0 0000 0 00 26 67 53 33 80 00 Separation Distance
115. hat next appears will depend on the type of file to be opened A text file will bring up the Import Text File dialog whereas spreadsheet database and HTML formats will bring up the Import Spread sheet dialog 44 Chapter 4 Importing Data from External Files Importing Text Files Choosing to import text files from the File Import Dialog brings up the window be low The contents of the file are displayed in the large preview area When the OK button is pressed the contents of the file are read into the GS Worksheet according to rules specified by the chosen File Format These rules define how many rows of header data precede the data rows 2 in the example below how missing values are identified with the number 99 in the example below how column names are separated with commas below and how data fields columns are separated from one another within data records with spaces in this example A different dialog window is available for importing spreadsheet database and HTML files described later Import Text File 0 xl File name G GSWin 32 Version 9YWorking files Demo2d txt Cancel File Format Column Assignments custom Properties 011 X2 Y 3 Z4 Change Demo2d Gilkey field Tab delimited text file sample m east m north Pb Al Ur 1 d li 422 696025 99 2 454 553567 6 912824 3 86 099424 99 4 99 99 5 6 147 872313 5 626897 329 763340 99 7 127 563145 99 8 99 3 99
116. hough cross variate analysis is not available for every autocorrelation measure If Z or Z2 are undefined the menu command will be dimmed Interpolate Menu The Interpolate menu provides access to one of the four major types of Interpolation provided by GS GS Geostatistics for the Environmental Sciences File Edi Data Autocorrelation Interpolate Map Window Kriging p CoKriging Inverse Distance Weighting IDW Simulation Kriging display the Interpolation Window with access to Kriging Cokriging display the Interpolation Window with access to Cokriging Inverse Distance Weighting IDW display the Interpolation Window with ac cess to Inverse Distance Weighting and Normal Distance Weighting interpola tion Simulation display the Interpolation Window with access to Conditional Simu lation The Map Menu The Map menu provides access to GS mapping functions 20 GS Geostatistics for the Environmental Sciences File Edit Data Autocorrelation Interpolate Map Window Help DEAS amp B BS 19 39 i 20 Map bz 1 Transect 3 d Map display the Mapping window with 3 d mapping selected 2 Map display the Mapping window with 2 d mapping selected Chapter 2 Getting Started 1 d Transect display the Mapping window with 1 d mapping selected if a 2 dimensional map file one having both an x and a y coordinate is currently se lected the 1 d option
117. ia the Mapping window when the variate to be mapped has only one X dimension ELDTITUCTTOMAREEE 9 iind File Demo1d dat Mouse Action C Scale C Zoom Reset Mouse Location X 38 8 Z 3 30 mean daily C Transect Image with Standard Deviation A transect with standard deviations can be drawn if interpolation files contain stand ard deviations Krig or Conditional Simulation files in GS format Transect Image mean daily C nml x File Demo1d dat Mouse Action pi Move C Scale C Zoom Reset Mouse Location X 50 3 Z 1 07 mean daily C Commands in this Window are the same as for earlier graphs 157 Chapter 15 Bibliography Chapter 15 Bibliography The following references may be useful for those seeking further background about geostatistics and its use in the environmental sciences 158 Burrough P A 1981 Fractal dimensions of landscapes and other environmen tal data Nature 294 240 242 Burrough P A 1986 Principles of Geographical Information Systems for Land Resources Assessment Oxford University Press Oxford Burgess T M and R Webster 1980a Optimal interpolation and isarithmic mapping of soil properties The semivariogram and punctual kriging Journal of Soil Science 31 315 331 Burgess T M and R Webster 1980a Optimal interpolation and isarithmic mapping of soil properties Il Block kriging Journal of Soil Science
118. ields in the data file Col 51 Chapter 4 Importing Data from External Files umns can also be assigned later from the Data Worksheet window Input File Formats File Import Properties Choosing to import files from the Import Text File or Import Spreadsheet dialogs brings up the File Import Properties window below File Import Properties X Data Records Header Records Field Column Delimiter Number of Header Records Table cells m 1 first row in table Y Missing Value Indicator Title Column Name Delimiter Numeric indicator hd rase cells Value 99 _ Data Records The Field Column Delimiter specifies how individual values within the data records are formatted For text files values can be comma separated tab separated space separated free format character separated or binary data When spreadsheets are imported columns are delimited by Table Cells only The Missing Value Indicator specifies the value or character within the file that in dicates that a value is missing and that the record should be ignored during import ing A missing value that is imported becomes a blank cell in the GS Data Work sheet The indicator can be absent a decimal point a numeric value or a character Header Records The Number of Header Records indicates whether the first records in the file con tain header records descriptive text that should be ignored as the file is read into the Data Worksheet
119. ifferent seed Smoothing Factor 0 0 M Use multigrid refinements oe z Default to Normal Distance Weighting NDW 1000 4 Interpolation Output I Report std deviation not variance M Draw map after interpolating Cycle faster on x than y Global Reset Cancel Save Exit Reset The Reset command returns all user default values on this tab to original default values To reset all values on all tabs use the Global Reset command at the bot 26 Chapter 2 Getting Started tom of the window Autocorrelation Defaults Offset start of first lag by 1 2 interval with this check box GS will when automatically defining regular interval lag classes shift the first lag class to 2 of its normal separation distance This can provide better resolved vario grams when there are sufficient pairs of points in shorter separation distance classes The disadvantage is that if there are few pairs of points for the shortest distance classes when the first lag is not offset a common problem there will be even fewer pairs available with the first lag offset lf this is the case there will be little if any improvement to the variogram Active lag 96 of maximum The Active Lag Distance specifies the range over which semivariance will be calculated The default active lag is some percentage of the maximum lag specified here This is not likely to be the most appropriate active lag for your data but
120. ific types 25 Chapter 2 Getting Started Places Past Decimal to Show When importing data files report this many places past the decimal in the Data Worksheet cells This value is overridden when specifying places past the decimal in the Field Column Assignment Dialog of the Data Worksheet window Automatically Rebuild Data Arrays When new data is imported and when columns are reassigned e g when the X Coordinate column is reassigned to column 3 from column 2 the internal data array used by GS must be rebuilt This can take some time if the array is big because duplicates must be checked missing values tested and autocorrelation boundaries calculated The alternative to automatic recalculation is to press the Rebuild button on the Data Worksheet Window Check or uncheck these boxes to turn off automat ic array rebuilds Global Reset Sets all user default values on all tabs to original default values User Preferences Analyses Tab The Preferences Analyses dialog window allows you to set user default values for some analyses x General Data File Import Reset r Autocorrelation Defaults Offset start of first lag by 1 2 interval Active lag 96 of maximum 5023 Automatically make anisotropic surface map Number of lag intervals 15 5 n Automatically subsample large data sets Number of subsamples 10000 IDW Interpolation Defaults Simulation Defaults Weighting Power 0 100 1 Use d
121. ill be returned to their pre build state Also take this action for other duplicates of this build Checking this box causes other duplicates encountered to be treated the same as this set of duplicates For data sets with many duplicate values this option saves time by keeping this dialog window from displaying again during the present build Cancel Cancel the data build Any duplicates set to missing values during this build will be reset to nonmissing 43 Chapter 4 Importing Data from External Files Chapter 4 Importing Data from External Files File Import Dialog A number of different file types can be imported into GS These include spread sheets e g Microsoft Excel formats databases e g Microsoft Access formats HTML web pages and text files Files are imported via the Import command within the Data Worksheet Window which brings up the dialog box below From this dia log you choose the file and the format as illustrated in the pull down list box at the bottom of the menu Select File 2 x Look in 3 GSWin70 ck Ee A 3 Cokrig xls E Demo xis My Recent Desktop Y My Documents pE GPRTPOS Excel Files xis Excel Files xls Lotus 1 2 3files wk Text Files xt dat csv Access Database Files mdb dBase Files dbf FoxPro Files dbf Paradox Files db HTML Tables htm html Open Press Open to open the identified file The window t
122. imates are made based on values at nearby locations weighted only by distance from the interpolation location Neither IDW nor NDW make assumptions about spatial relationships except the basic as sumption that nearby points ought to be more closely related than distant points to the value at the interpolate location IDW applies stronger weights to nearby points than does NDW The formula used for Inverse Distance Weighting is Zest 2 s X 1 hj s where Zest estimated value for location Zi measured sample value at point i hj distance between Zest and z s smoothing factor and p weighting power The formula used for Normal Distance Weighting is the same as that for IDW except that the denominator distance plus smoothing factor rather than inverse of dis tance plus smoothing factor The weighting power p defines the rate at which weights fall off with hi the distance between the interpolated and sample locations A value of 1 5 is typical The smoothing factor s reduces the likelihood that any one sample value will overly influence an estimated value for a given interpolation location IDW is an exact in terpolator so where an interpolation location j coincides with a sample location Zest z and a sharp peak or valley may result setting s gt 0 reduces this peak ing effect when it occurs The Interpolation Window contains the IDW tab 140 Chapter 12 Inverse and Normal Distanc
123. in in the NW corner of the grid The following listing is for the first few coordinates in a standard GSLib for mat file The first record shown on 2 lines because it is too long to display on one line identifies the file as a GSLib output file and provides coordinate spacing information Record two states that there are 3 fields per record and records 3 5 provide the names of the fields GS Output Punctual Kriging Interpolation File v9 0 GSLib format nx 3 xmin 5 0000 xsiz 10 0000 ny 6 ymin 5 0000 ysiz 10 0000 3 Z Estimate EstimationVariance Neighbors 3 98 6 7825 8 0 34 5 1996 8 1 45 4 5482 8 3 14 5 2250 8 7 67 4 8409 8 0 61 6 2536 8 1 05 4 8234 8 0 86 5 1885 8 3 41 3 9369 8 1 03 5 7149 8 1 44 5 7889 8 2 14 6 2928 8 1 53 6 2740 8 1 15 4 7431 8 0 98 7 2801 8 2 29 9 9600 8 2 28 9 9919 8 2 10 9 9002 8 145 Chapter 14 Mapping Chapter 14 Mapping GS produces 2 d and 3 maps of spatial data following interpolation The data to be mapped come from kriging or IDW analysis and are thus contained in interpola tion output files Maps can be displayed in a variety of ways with a variety of differ ent contouring schemes 3 dimensional maps can be rotated on the fly and both 2 dimensional and 3 dimensional maps can be zoomed to more closely view a transi tion or other map feature Additionally sample postings original data locations can be displayed and estimation standard errors can be mapped for input
124. in the Autocorrelation Analyses windows There is a sep arate autocorrelation window for the primary variate Z for the secondary variate Z2 and for the cross variate Z x Z2 Here in the Cokriging window you can specify whether to use the isotropic or anisotropic model for each of these variograms You can also choose to use a relative variogram in which the nugget and structural components are rescaled from 0 to 1 0 for each of the three models Discretization grid Choose either Point or Block cokriging in this section The choices in this section are the same as for Kriging above Search Neighborhood Covariate The search strategy for covariate Z2 values in cokriging can be different from that for the primary variate Z values In the Search Neighborhood Covariate tab you can specify whether search parameters should be the same as for the primary variate Z or different See Search Strategy in Chapter 9 for further information about the op tions available Search Primary Variate Covariate Same as primary Neighborhood Shape Number of Neighbors Round gt cc Radius 98 66 Minimum 1 E Elliptical d Maximum 16 zd dul rds Maximum 2 139 Chapter 12 Inverse and Normal Distance Weighting Chapter 12 Inverse IDW and Normal NDW Distance Weighting Inverse Distance Weighting IDW and Normal Distance Weighting NDW are inter polation techniques in which interpolated est
125. ing value Cells can be assigned temporarily missing by right clicking on them a sec ond right click returns them to non missing In Input and Output files missing values are indicated by characters or values e g 99 defined in the Preferences window Model Parameters See Variogram Model Parameters No Header Records The first record of the file contains numeric records that should be treated as data Number of Header Records are Fixed An input field beneath the list box appears when this choice is made and this field specifies the number of records at the top of the file to consider descriptive text when reading the file the first data record is the next record Number of Header Records Varies The number of header records will be assumed to be all records prior to the first all numeric record If all records contain an alphanumeric Sample ID field then all rec ords will be assumed to be header records and no data records will be read In the example below there are 2 header records File GMD Test Site m east m north Pb pH 34 5 45 6 0 231 5 8 36 46 5 0 241 5 9 Numeric Value as a Missing Value Indicator The indicator value that will appear when a numeric value is specified in the list box The example below presumes that 99 has been specified the missing value indica tor and thus the third value of this record will be read into the worksheet as a miss ing value 13 2 34 5 99 0 0 15 Parameter File
126. irst record contains coordinate interval information that is read by GS when mapping GSLib files The second record of the file specifies three header records named estimate estimation variance or standard deviation and neighbors Records that follow are in the same order as for Surfer but there are three fields per record esti mate estimation error and number of neighbors rather than just one field the Z estimate See a detailed example in Chapter 11 Map Grid X direction the range within the file for values in the x horizontal direction Y direction the range within the file for values in the y vertical direction for 1 dimensional data sets this field is blank Z values the range of estimated Z values in the input file 147 Chapter 14 Mapping Z SD values the range of estimation Z standard deviation values in the input file only when input files are in a GS format that contain both Z values and Z standard deviation values will this box be selectable N N missing the number of valid records in the file and in parentheses the number of missing values The default missing value indicator e g 999 is specified in the Preferences General dialog the active missing value indicator for map files is indicated in the Map Contour Intervals window Missing values are mapped as transparent regions Exclusive polygons are mapped as miss ing values as is any interpolate location for which
127. is placed around the interpolation point when kriging The interpolation esti mate for that point is based on the mean value of estimates for each of the discreti zation grid points You may specify the number of discretization grid points to use in the X and Y boxes 2 points in the X direction and 2 points in the Y direction means that 4 discretization points will be used The size of the discretization grid depends on the interpolation grid For a regular grid the size is equivalent to the X and Y direction distance intervals respectively see Defining a Regular Interpolation Grid in Chapter 9 For an irregular grid the size is specified in the Define Interpolation Grid worksheet see Block Size under 136 Chapter 11 Kriging and Cokriging Defining an irregular Interpolation Grid in Chapter 9 Cokriging Cokriging is an interpolation technique that allows one to better estimate map values if the distribution of a secondary variate is known The secondary variate also called a covariate or Z2 is sampled from the same locations as the primary variate Z and also from a number of additional locations If the primary variate is difficult or ex pensive to measure then cokriging can greatly improve interpolation estimates with out having to more intensely sample the primary variate Consider the following hypothetical example After a radioactive spill plutonium was sampled across an 80 x 80 m area at a sample density indicated by th
128. isotropic axis 93 Printing graphs 35 setup 17 worksheets 35 Punctual cokriging 140 Punctual kriging 137 167 Quotes as column title separators 52 Range 79 80 86 87 167 168 Rebuild command 38 Records See Data records Regression cross validation 129 174 regression analysis 67 68 regression coefficient 81 88 regression values 69 Regular interpolation grid 118 122 Regular lag interval classes 168 Relative variogram 137 140 Residual sums of squares 81 88 Right click menu 23 Rodograms 98 Rotate graph 153 155 Sample ID 39 167 Sample postings See Coordinate postings Sample variance 74 Scaling data 54 Screen layout 15 Search neighborhood 120 nearest neighbors 120 octant search 121 radius 121 Secondary variate Z2 138 Seed value 28 Semivariance capacity 72 overview 70 semivariance analysis window 71 semivariance offset 70 values 78 variograms window 77 Serial number 7 8 Sill 79 80 86 87 167 Simple cokriging 140 Simple kriging 137 Single user license agreement 12 Site licensing 12 Smoothing factor 28 141 142 Sort 18 Space separated free format values 52 Spaces as column title separators 52 Specific shapes 119 Spherical anisotropic model 88 Spherical isotropic model 82 Spreadsheet input files 44 51 52 Standard deviations map 154 Index Standardized ordinary cokriging 140 Standardized variogram 96 Structural variance 79 163 167 Subsa
129. isplay the data worksheet window e Assign Column assign a variate to a data sheet column e sort the highlighted column the sort alternates between ascending and descending order If the cursor is not in a worksheet cell the sort com mand will be dimmed e Change Decimals increase or decrease the number of decimal places to show in a particular column this has no effect on calculations which are al ways performed in double precision arithmetic The cursor must be in an ac tive worksheet window or these commands will be dimmed e Insert insert a row or column into the active worksheet e Delete delete a row or column in the active worksheet e Import Data import a data file into the active worksheet e Export Data export the contents of either the active worksheet or the active data arrays to an external file The active data arrays are the non missing da ta in the ID X Coordinate Y Coordinate Z data and Drift columns of the Da ta Worksheet window If the Z data have been transformed using a trans formation command the transformed z values will be printed in addition to the original z values in the Data Worksheet Data can be exported as tab separated text files txt comma separated value text files csv Excel spreadsheet files xls html text files htm or xml files xml 18 Chapter 2 Getting Started e List Graph Values display the graphed data This command will be dimmed
130. king the left mouse button and dragging the cursor Scale shrinks the graph image with the left mouse button Zoom allows you to zoom in on a particular graph area by using the left mouse button to define a rectangular zoom area Within the zoomed area the location of the cursor is noted on the Mouse Location panel Reset resets the image to the default rotation angle and scale 93 Chapter 6 Semivariance Analysis Overview Mouse Location Provides information on the current location of the cursor when it is on the map sur face Units are map units as specified by the axes Z is semivariance Anisotropic Semivariance Surface 3 d Variogram Map The 3 d Anisotropic Semivariance Surface or Variogram Map is a 3 d projection of the 2 d map Use the Edit Graph command to change 3 d graph formats Anisotropic Variogram Map Pb E lol M azimuth 22 ad 348 Semiverisnce 1382 1 299 Set 1 207 1104 0 27311 1 021 0 828 Mouse Action 0 825 0 743 Off 0 650 0 557 Reset pe Reset 0 371 0 278 Mouse Location 0 093 33 39 pmo Y 32 44 Z 0 524 Commands for the 3 d map projection are the same as those for the 2 d projection above 94 Chapter 6 Semivariance Analysis Overview Cross Autocorrelation or Cross Semivariance Analysis The Cross Autocorrelation Analysis Window is identical to the Autocorrelation Anal ysis window except that cross semivarianc
131. kknife anal ysis In cross validation analysis each measured point in the spatial domain is indi vidually removed from the domain and its value estimated as though it were never there Then the point is replaced and the next point is removed and estimated and so on In this way a graph can be constructed of estimated vs actual values for each sample location in the domain In Jackknife analysis estimates are compared against measured values for a set of locations different from those used as input data The jackknife data are specified in a worksheet that appears when the Define command is pressed Each of these validation analyses are described more thoroughly below 120 Chapter 9 Interpolation Basics Define Z Estimate Boundaries The Z Estimate Boundaries window is used to constrain estimated Z values interpo lates to a specific range It is accessed from the Interpolation Window Z Estimate Boundaries E x Z Data Range Range to Use for Estimated Z 0 06 1 25 0 00 125 Reset Cane OK Range to Use for Estimated Z Enter the lowest permissible value for estimated Z in the left hand box and the highest permissible value in the right hand box In this example if the interpolation System were to estimate a value of 0 45 for a particular point the value will be re ported as 0 Reset Reset values to the lowest and highest data values respectively OK Cancel Press OK to save changes and close the window p
132. late Map Window Help 1 New File Ct N 87 Open File Ciri 0 E Save File Ctr S Save File As Printer Setup Prt Ctri P Export Graph Preferences Exi Cti G 1G Demo2d 2Dimensional Analysis V9 par 2 G Demo2d 2Dimensional Analysis V7 par e New File Clears existing analysis parameters e Open File Allows the user to load an existing parameter file To open a text data file use the Import Command in the Worksheet window e Save File Save the existing parameter file e Save File As Save analysis parameters in a file to be named 16 Chapter 2 Getting Started Printer Setup Make changes to the print format Print Prints a spreadsheet or graph You can also access this command by right clicking on a graph or spreadsheet Export Graph Save graph to file you can also access this command by right clicking on a graph Preferences Set user preferences to be saved from session to session Exit Exit GS The Edit Menu The Edit menu provides access to the cut copy paste delete editing commands These commands are available whenever the cursor is in an editable field within a particular window GS Geostatistics for the Environmental Sciences Demo2d 2Di Edt Data Autocorrelation Interpolate Map Window Help De cx Dee se E gt dik bile t E Copy Ctrl C Ig Paste Ctrl V Delete Del Sedet Ci T
133. lds each of the indi vidual analysis windows that are currently open The main windows are The Data Worksheet Window The Data Summary Window The Autocorrelation Window The Interpolation Window The Map Window Chapter 2 Getting Started Main Menu The Main Menu presents access to the windows that provide GS analyses Below the command menus are icons that represent short cuts to many of these functions GS4 Geostatistics for the Environmental Sciences Demo2d Cokrig par File Edit Data Autocorrelation Interpolate Map Window Help DSHS 5 4 4 gt vv M x u i B Commands and toolbar buttons that are shaded out are not selectable For exam ple the print icon is not available when viewing a window without a graphic or work sheet to print The six covariate icons for covariate functions are not available un less a covariate has been defined in the Data Worksheet window The tool bar is customizable via the Edit menu or by right clicking on the main menu You may add or remove shortcut icons for most analyses It is also movable and reconfigurable it can be dragged to any spot on the screen with the mouse The File Menu The File Menu provides commands for saving and retrieving GS parameter files used to store and retrieve analysis settings and also commands for printing and Setting user preferences GS Geostatistics for the Environmental Sciences Demo2d 2Dim File Edit Data Autocorrelation Interpo
134. le descriptive statistics for the variates defined in the Data Worksheet window Information is provided for both the X Y Coordinates as below for the Z variate in a separate Z Variate tab described earlier and in a Regression tab when a covariate is assigned described later x p Range x direction 0 60 79 30 y direction 1 50 79 00 Coordinates Range and Name This is the range over which the x direction and y direction data vary and the name of the variates as defined in the Data Worksheet Posting The posting is a map of the location of each x y coordinate point within the range of X and Y coordinate values For 1 dimensional transects the posting appears as points along a straight line Press Expand or click on the map image to bring up a larger Covariate Postings Quantile Plots window that provides access to legends and different ways of grouping quantile data see below Data postings of kriged data are also available from the Map window 62 Chapter 5 Summary Statistics Coordinate Postings Quantile Plots 2 d Scattergrams The Coordinate Posting provides a map of sample locations that can be coded to show sample values at that location Values are grouped into as many as 10 sym bol classes Coordinate Posting Pb 1 inl xl Levels Number B C Intervals Pb Quartiles C Custom lt 0 23 Define lt 0 34 0 51 Mouse Action 1 25 Data
135. lue either move the slider be neath it or type a new value directly into the text box Nugget Variance or C the y intercept of the model the nugget variance can never be greater than the sill Sill or the model asymptote the sill can never be less than the nugget variance Range A the separation distance over which spatial dependence is appar ent This is sometimes called Effective Range in order to distinguish range A from a model s range parameter Ao The Range A is calculated from as de scribed in the formulas for the different models below The range cannot be less than 0 Statistics This Fit GS provides three statistics to aid the interpretation of model output 80 Chapter 6 Semivariance Analysis Overview Residual Sums of Squares provides an exact measure of how well the mod el fits the variogram data the lower the reduced sums of squares the better the model fits When GS autofits the model it uses RSS to choose parameters for each of the variogram models by determining a combination of parameter val ues that minimizes RSS for any given model The Residual SS displayed in the This Fit box is calculated for the currently defined model r provides an indication of how well the model fits the variogram data this value is not as sensitive or robust as the Residual SS value for best fit calcula tions use RSS to judge the effect of changes in model parameters Proportion
136. mals icon or use the Data Change Decimals menu command Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 69 Chapter 6 Semivariance Analysis Overview Chapter 6 Semivariance Analysis Overview Semivariance is an autocorrelation statistic defined as y h 1 2N A EL zi Zan where y h Semivariance for interval distance class h 2 measured sample value at point Zin measured sample value at point h and N h total number of sample couples for the lag interval h Semivariance is evaluated in GS by calculating y h for all possible pairs of points in the data set and assigning each pair to an interval class h For regular interval clas ses GS makes interval class assignments for any given pair of points using the following formula class INT D DI 1 where D distance separating the pair DI lag class distance interval INT Integer function Where the first lag is offset by 12 interval in order to better resolve values close to the origin the formula is class INT D DI 40 5 1 This option is available by checking a box in the Preferences Analyses dialog It can provide better resolved variograms when there are sufficient pairs of points at shorter separation distances The di
137. mpled data 27 Summary statistics 54 Surface 149 Surfer grid output file format 120 map input files 50 145 Map input files 148 Surfer XYZ input file format 46 Symbols 32 66 Tab separated values 52 Tabs as column title separators 52 Text files 44 45 Tick marks 31 Title 38 Tool bar 16 Transect image 158 Transfer license 22 Transformations assigning 54 backtransformations 55 162 definition 168 lognormal 54 offsets 55 scaling 0 1 54 square root 54 Trend 99 Universal kriging 136 Updates 12 22 Validation analysis 121 cross validation analysis 129 jackknife analysis 129 Variance cloud analysis 77 cloud pairs 112 Variate assignments 38 Variate names 38 47 163 164 167 168 Variogram Ao 79 80 86 87 167 active lag default 27 anisotropic models 86 anisotropy surface 27 79 80 86 87 capacity 72 defaults 27 effective range 79 80 86 87 167 isotropic models 79 80 map 73 92 94 model command 74 model parameters 80 168 model type for kriging 137 140 nugget variance 79 80 86 87 number of lag intervals 27 offset 27 options 74 range 79 80 86 87 167 sill 79 80 86 87 167 structural variance 79 167 subsample data 27 values 78 variograms window 77 Variography 70 Vertices 126 Warnings 24 Warranty 13 Weighting power 28 141 142 Window menu 21 Worksheets capacity 39 formulas 39 jackknife data 121 limits 39 printing 35 sorti
138. mporarily or permanently deleted from sub sequent analyses Field assignments assigning fields or columns to x coordinate values y coordinate values etc are made in the worksheet window by clicking on the second row C Documents and Settings Demo xis Data Worksheet O x Base Input File Import file _ Rebuild LI Fler Clear Data Title Description Field 4 Trebilithia Regional Authority Field Column Number click Sample protocol 15A Field Column to sort values in column Assignment click to Field Column Name click to change m east m north 4 50 11 90 n 23 40 i Temporary missing value right click 32 60 i to toggle between missing red and 44 50 non missing black 64 00 71 80 3 50 10 20 16 30 27 20 4 20 Base Input File The Base Input File is the external file from which worksheet data first were loaded if none of the data were loaded from an external file then this field will be blank To import data to the worksheet from an external file press Import to bring up a File Import Dialog window Note that the data in the worksheet may not be the same as data in the Base Input File if the worksheet data were changed after importing Import File Press Import File to bring up a File Import dialog from which text and binary e g worksheet files can be imported into the worksheet see Chapter 4 37 Chapter 3 Working with Data Reb
139. ms 97 menu 19 moran s I analysis 106 number of lag intervals 27 offset 27 pairwise relative variograms 104 rodograms 98 semivariance 70 standardized variograms 96 subsample data 27 Axis formats 32 orientation 73 Azimuth 93 Backtransformations 55 162 Base input file 37 Bibliography 159 Binary data record format 163 Block cokriging 140 kriging 124 137 163 size 124 Co 79 163 Cartesian x y coordinate system 15 169 Ceiling 34 150 Character separated values csv 163 Clear 38 Cokriging 41 71 121 138 Cokriging type 139 169 Index Column 38 field assignments 37 39 titles 47 163 164 167 168 widths 39 Commas as column title separators 52 Conditional simulation 117 121 132 colocated cokriging 133 external drift 133 interpolation defaults 28 multigrid refinements 28 number of simulations 28 135 residuals 133 secondray data 133 134 seed value 28 Context menu 23 Contour levels 34 150 151 Convert GS DOS File 35 Coordinate postings 62 1 d scattergrams 65 definition 167 map data 149 157 posting intervals 66 Coordinates assigning 39 cartesian 169 latitude longitude 169 Copying data and graphs 35 Correlograms 100 Covariance analysis 101 Covariate Z2 assignment 40 definition 164 169 icons 16 regression 67 values warning 41 Cross semivariance analysis 20 95 139 Cross validation analysis 121 129 values 1
140. mulation unique to a specific run The default is specified in the Preferences dialog In either case a different random path is used for each simulation Multigrid refinements Checking this box forces the analysis to follow a step wise procedure when simulating interpolation nodes In the first step a coarse grid is used to allow the influence of large scale variogram structure in subse quent steps the search neighborhoods are smaller This avoids the need for ex tensive conditioning The default is specified in the Preferences dialog Secondary data Collocated secondary data can be used to refine estimations Collocated means that a secondary data value is available for every grid node to be estimated not simply for every primary data value as is the case for regular cokriging 132 Residuals This is the same as simple kriging with a locally varying mean Press the Define button to define the residuals to be used External drift Press the Define button to define the drift values Collocated cokriging Press the Define button to define the covariate values Chapter 10 Conditional Simulation Secondary Data for Simulations Secondary data for conditional simulation are defined in the Simulation Secondary Data window Secondary data must be available for every grid node to be estimated This window is accessed from the Secondary data tab of the Simulate tab Locally Varying Mean Values Locally Varying Means
141. mum lag interval is approached GS allows 1 million lag classes to be specified with up to 1 billion pairs per class Lag Class Distance Interval The Lag Class Distance Interval defines how pairs of points will be grouped into lag classes Each point in a variogram represents the average semivariance for a single lag class which is a group of pairs separated by a certain Lag Class Distance Inter val sometimes called a step size This interval can either be calculated by GS in which case it will be regularly distributed across the active lag distance or it can be manually set by the user e Use individually specified points With this option you may use the Define command to bring up a window to Define Lag Class Intervals i e to specify individual break points for the lag intervals described below e Use a regular interval With this option the value specified is the size of the interval applied regu larly across the active lag distance E G an interval of 2 units with an active lag distance of 10 units will create 5 lag classes each 2 units wide The minimum interval allowed is the smallest distance separating any two sam ple point locations in the data set The maximum interval is the greatest dis tance separating any two sample point locations The default value is 10 of the active lag or if 10 of the active lag is smaller than the minimum al lowed the minimum allowed This default may not be appropriate for any given data
142. n Matheron G 1971 The theory of regionalized variables and its applications Cahiers du Centre de Morphologie Mathematique Fontainebleau No 5 Nielsen D R and O Wendroth 2003 Spatial and Temporal Statistics Sam pling Field Soils and their Vegetation Castena Verlag Reiskirchen Germany Robertson G P 1987 Geostatistics in ecology interpolating with known vari ance Ecology 68 744 748 Robertson G P and K L Gross 1994 Assessing the heterogeneity of below ground resources Quantifying pattern and scale Pages 237 253 in M M Caldwell and R W Pearcy eds Plant Exploitation of Environmental Heteroge neity Academic Press New York New York USA Rossi R E D J Mulla A G Journel and E H Franz 1992 Geostatistical tools for modeling and interpreting ecological spatial dependence Ecological Monographs 62 277 314 Sokal R R and N L Oden 1978 Spatial autocorrelation in biology 1 Method ology 2 Some biological implications and four applications of evolutionary and ecological interest Biological Journal of the Linnean Society 10 199 228 Trangmar B B R S Yost and G Uehara 1985 Applications of geostatistics to spatial studies of soil properties Pages 45 94 jn N C Brady editor Advances in Agronomy Volume 38 Academic Press New York Vieira S R J L Hatfield D R Nielsen and J W Biggar 1983 Geostatistical theory and application to variability of some agronomical properties
143. n that comes with ArvView or the full version that comes with Arclnfo M a Open ArcToolbox b Choose the Import to Raster tool c Specify the GS output file name the grid type integer or floating point the name of the grid output file and press OK d You may now open the file in ArcMap 143 Chapter 13 Interpolation Output File Formats Surfer Grid GRD Format The Surfer Grid grd Krig Output format or Map Input format has a short header area that provides information needed for mapping and the data is then written as a continuous stream of Z estimates beginning from a specific corner of the interpola tion grid The standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format This format is compatible with Golden Software s Surfer mapping program Note that the Surfer Grid format is different from the Surfer XYZ format used for input files see Chapter 4 The following listing is for the first 100 or so coordinates in a standard Surf 144 er Grid format file The first record is a required line of code letters that identifies the file as a Surfer grid file Record two contains the number of grid lines along the x axis and y axis respectively Record 3 contains the minimum and maximum values of the x coordinate Record 4 contains the minimum and maximum values of the y coordinate Record 5 contains the minimum and maximum values for the z va
144. nd Define Variance Std Deviation C Simple Stationary Nonstationary Dene Search Primary Variate Covariate retener Demem Estimate trend Number of Neighbors Neighborhood Shape Minimum Round Radius 102 60 Isotropic Maximum 16 C Anisotropic Use Relative 21 C Elliptical ape r Discretization Angle N 0 m ries as Octant Search Point Kriging Maximum 2 H Length 102 60 zl Block Kriging Nidth ES gt Width 102 60 x 2 mM 2 Interpolation Range Defines where to place interpolation estimates in a regularly spaced grid across a rectangular area or at user specified locations in either case with or without masks that can define areas to include or exclude Regular x y grid specified intervals A grid is defined by a rectangle that has an X direction length a Y direction length and for each direction intervals between the grid intersections Interpo 117 Chapter 9 Interpolation Basics lation locations are at every grid intersection The default range is defined by the minimum and maximum X coordinate and Y coordinate values and an interval based on a certain number of points in each direction For 1 dimensional data sets there is no y direction The grid can be changed with the Define command which will display an Inter polation Grid dialog window Irregular x y g
145. ng 39 window 37 X axis range 31 X coordinate assignment 39 40 defintion 169 xls files 18 35 xml files 18 35 Y axis range 31 Y coordinate assignment 39 40 175 Index defintion 169 assignment 39 40 Z primary variate definition 164 169 assignment 39 40 icons 16 axis range 32 regression 67 definition 169 values warning 41 estimate boundaries 122 Zoom 153 Z2 covariate 176
146. nsferring your license you will not be able to open GS again until it is reactivated on the same or a different computer You must be connected the internet in order to deactivate Deactivate 65 License Deactivation 2 When you deactivate your license it is returned to the activation server for later use You will not be able to use GS until it is reactivated with the original license number Please enter your license number activation code Use proxy server Address examples proxy mycompany com or 292 191 22 3 Port Deactivate License Number activation code Enter the license number also called activation code This number is on the CD sleeve or in the purchase confirmation email that you received Use Proxy Server Check this box to connect to the internet using the proxy address and port specified Address Specify the proxy address to use Valid formats include a proxy mycompany com or b 192 191 22 33 Get the correct address from your network administrator Port Specify a port to use for the proxy server Get the correct port number from your network administrator 11 Chapter 2 Getting Started Deactivate Deactivate the current license Once you deactivate you may not run GS again this computer without activating it again There is no limit on the number of times you may deactivate and re activate Updates Maintenance updates are available free of charge t
147. nsion D for the data set defined in the Data Defini tion Menu GS calculates the fractal dimension D as a function of the slope of a log log variogram plot Burrough 1981 1986 D 2 m 2 where D the Hausdorff Besicovitch statistic and m the slope of a log log variogram Because D is based on an analysis of semivariance it is sensitive to the same anal ysis parameters that affect semivariance analysis Fractal variograms both isotropic and anisotropic appear in the Autocorrelation Window on the Fractal tab Press the Expand button on this tab to bring up the Fractal window Fractal Variograms Pb EE ici xl Pb Isotropic Analysis 0 424 T 2 0 510 2 2 0 597 E 0 684 5 0 771 o 0 00 0 63 1 25 1 88 log Separation Distance h DO 1 836 SE 0 223 r2 0 895 n 10 Isotropic 45 Degrees 90 lt gt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 106 Chapter 8 Variance Clouds and h Scattergrams Chapter 8 Variance Clouds and h Scattergrams Variograms can be sensitive to outlier values in a data set and sometimes an errat ic looking variogram can be traced to a single extreme value that inflates y h when ever they are compared with other values One way to locate such outliers is to draw a variance cloud for each separation di
148. nventional measure of autocorrelation similar in inter pretation to the Pearson s Product Moment correlation statistic for independent samples in that both statistics range between 1 0 and 1 0 depending on the degree and direction of correlation The statistic is defined as A XZXz Zen E where I h autocorrelation for interval distance class A 2 the measured sample value at point and Zi the measured sample value at point h Note that in this analysis all of the weights in the adjacency matrix Sokal and Oden 1978 are set to 1 i e is weighted by distance h between sample points rather than by simple adjacency Calculating this statistic for a variety of lag distances yields the Moran s autocorrelogram Moran s I correlograms both isotropic and anisotropic appear in the Autocorrelation Window on the Moran s tab Press the Expand button on this tab to bring up the Morans s window 815 Pb Isotropic Moran s Moran s 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90 Degre lt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 105 Chapter 7 Other Autocorrelation Measures Fractal Analysis The Fractal Analysis window is used to set up the parameters for fractal analysis and then calculate the fractal dime
149. o registered users Update files are available by download only from http www gammadesign com The current version of GS can be checked from the Help menu as described in Chapter 2 Licensing Site Licensing If you have reason to install GS on more than one computer in the same laboratory or on a network that allows more than one user at a time to access the program please contact Gamma Design for information about converting your single user license to a laboratory group license 5 computer or a single building site license unlimited computers in the same physical building It is a violation of your sin gle user license agreement if the program resides on more than one comput er Single User 1 computer License Agreement Please read carefully this is a legal End User License Agreement EULA between you the end user and Gamma Design Software LLC Gamma Design Software When you install this software on your computer you signal your agreement to be bound by the terms of this agreement including the Software License and the Limited Warranty If you do not agree to be bound by the terms of this agreement do not install the software and return the package together with accompanying written material to Gamma Design Software at the address below for a full refund 1 Gamma Design Software retains ownership of the GS program enclosed Gamma Design Software gives you the end user the right to use a single copy of GS on a sin
150. of the labels font precision etc see the Axis Titles Labels tab Y Axis Range and Tick Marks The y axis range is set identically to the x axis range Note that for maps of 1 dimensional transects there is no y axis the z axis represents the vertical dimen sion 31 Chapter 2 Getting Started Z Axis Range and Tick Marks The z axis range on maps is set identically to the X and Y Axes Note that a z axis is only present in maps and transects 1 d maps Bars For bar graphs you may specify the number of bars to be plotted their color and pattern The Bars section is not shown above Symbols For x y graphs e g variograms you may specify the type of symbol open box closed circle etc as well as the size and color of the symbol The Symbols section is not shown in the example screen above Graph Settings Axis Titles Labels Tab The Axis Titles and Labels tab of the Graph Settings Dialog Window allows you to specify the text that accompanies each axis and to format the values that accompa ny the major tick marks Graph Settings General Axis Scaling f Axis Format Title Decimals Exponential 2 ul X Axis m east 1 m E Y Axis m north Axis Lines width 1 v sides Font for Axis Titles Font for Axis Values Name Arial Name Arial Size 8 Size 8 Style Normal Change Style Normal Change Ap
151. om intervals as described below Mouse Action Off returns the mouse to normal operation Move allows the graph to be moved within the window by clicking the left mouse button and dragging the cursor Scale shrinks the graph image with the left mouse button Zoom allows you to zoom in on a particular graph area by using the left mouse button to define a rectangular zoom area Within the zoomed area the location of the cursor is noted on the Mouse Location panel Reset resets the image to the default rotation angle and scale Other Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu 64 Chapter 5 Summary Statistics 1 d Scattergrams The 1 d Coordinate Posting window provides a map of coordinate locations for 1 dimensional data The location of each data point in the active data set is marked by a symbol corresponding to its relative value Both the number of levels displayed as well as the range for each level is user defined A similar window provides post ings for 2 d data as described above Coordinate Posting mean daily C E Di xj File Demo1d dat Levels Number g u 0 Type Quanties C intervals C gt mean daily C Quartiles Custom 3 lt 1 00 Defne Mouse Action E Off Y Reset 1 00 121 67 242 33 363 00 day Commands in this window are the same as for 2 d
152. onal Simulation for further details Use multigrid refinements Checking this box forces the analysis to follow a stepwise procedure when simulating interpolation nodes by default See Chapter 10 Conditional Simulation for further details No of simulations specify the default number of simulations to perform See Chapter 10 Conditional Simulation for further details Interpolation Output 28 Draw map after interpolating check this box to automatically draw the map of interpolated values after interpolation Report std deviation not variance check this box to report standard deviation values rather than variance values for interpolation error terms This is a default condition that can be changed in the Interpolation Window see Chapter 9 Interpolation Basics for further information Cycle faster on x than y ordinarily 2 dimensional interpolation results are written to output files with y coordinate values cycling fastest e g in the x y order 10 2 10 3 10 4 10 5 20 2 20 3 20 4 20 5 check this box to write results with x coordinate values cycling faster e g 10 2 20 2 10 3 20 3 10 4 20 4 10 5 20 5 Chapter 2 Getting Started Global Reset Sets all user default values on all tabs to original GS defined default values Graph Settings General Tab The Graph Settings Dialog appears when you edit graphs The dialog will look slightly different depending on whether yo
153. ordinate and one z variate Note the four variate names in records 3 6 File for field 55 4 ID X meters y meters Z mm IL3 14036 309 7 11 14 13621 1266 25 22 12384 911 79 23 121276 978 91 24 12674 190 14 48 Chapter 4 Importing Data from External Files Text Input File Formats ArcView XYZ Format The ArcView input file format is comprised of header records and data records a Data records are comma delimited XYZ type data This means that each data record contains at least 3 fields x coordinate location a y coordinate location and the value for at least one z variate measured at that x y location single dimension transects will have only x coordinate and z variate data values Ad ditional fields can hold other variates for that location e g sample ID other measured z variates The ArcView XYZ input format is not the same as the Arcinfo Ascii Raster File Format which is a Kriging output format that can be read directly by Arcinfo or Arcview GIS software A single header record precedes the data records and contains field variate names for the data record fields Names are within quotes and comma delimited Missing values are indicated by blank fields Any of these parameters field delimiters number of header records missing value indicators etc can be changed to a custom format from the File Import Properties window The following listing is the first 9 records of a standard Arc
154. ou may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu Normal Probability Values The Normal Probability Listing window provides a listing of the values used to create the Normal Probability distribution All values in the data set are ranked by value ascending order any given row is the frequency of the value of that row plus all preceding frequencies expressed as percent lognormally transformed 60 Chapter 5 Summary Statistics In Pb In Cumulative Pct 2 813 0 247 2 659 0 446 2 120 0 852 2 040 1 139 2 040 1 363 1 966 1 545 1 897 1 699 1 897 1 833 1 897 1 950 1 897 2 056 1 897 2 151 1 833 2 238 1 833 2 318 1 833 2 392 1772 Actions You may Print Copy or Export the contents of the worksheet using the menu commands of the main GS window or via a right click menu You may also change the Decimal Places reported by highlighting a column and pressing the Increase or Decrease Decimals icon or use the Data Change Decimals menu commana Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location 61 Chapter 5 Summary Statistics Data Summary Window X Y Coordinates Tab The Data Summary provides simp
155. ouput variance 120 output files 143 144 145 146 type 136 with external drift 137 with trend 136 Lag class distance interval 27 70 71 72 75 165 Latitude 15 169 Legend title 66 License number 8 Linear anisotropic model 90 Linear isotropic model 84 Local grid 137 Longitude 15 169 Madograms 97 Main menu 16 Major axis 86 93 Map 2 d image 156 2 d sample postings 157 Index 3 d image 153 3 d standard deviation image 154 ArcView input files 144 148 ceiling 34 150 contour levels 34 150 151 estimation variance 140 floor 34 150 grid range 148 grid lines 34 150 GS input file format 143 GS input files 148 GSLib input files 146 input file formats 143 147 legend 34 150 mapping in GS 147 menu 20 mouse action 153 rotate graph 153 rotation 155 scale 153 standard deviation 149 surface 149 surface properties 33 Surfer input files 145 148 zoom 153 Mapping draw map after interpolating 28 interpolation window 118 Masks 119 Menus autocorrelation 19 context 23 data 18 edit 17 file 16 help 21 interpolate 20 krig 20 main 16 map 20 right click 23 window 21 Minor axis 86 Missing values count 140 definition 166 missing value indicator 24 41 45 47 49 50 51 52 143 149 151 permanent missing values 39 41 preferences 23 temporary missing values 39 41 43 Model parameters 80 87 Model results 77 Mor
156. p parent This is sometimes called Effective Range in order to distinguish range from a model s range parameter Az The minor range is calculated from as described in the formulas for the different models below The minor range can never be more than the major range Range Major the separation distance over which spatial dependence is ap parent In some texts this is called the Effective Range in order to distinguish range from the model s major range parameter A1 The minor range is calcu lated from A as described in the formulas for the different models below The major range can never be less than the minor range Statistics This Fit GS provides three statistics to aid the interpretation of model output 87 Chapter 6 Semivariance Analysis Overview Residual Sums of Squares provides an exact measure of how well the mod el fits the variogram data the lower the reduced sums of squares the better the model fits When GS autofits the model it uses RSS to choose parameters for each of the variogram models by determining the combination of parameter val ues that minimizes RSS for any given model The Residual SS displayed in the This Fit box is calculated for the currently defined model r provides an indication of how well the model fits the variogram data this value is not as sensitive or robust as the Residual SS value for best fit calcula tions use RSS to judge the effect of changes in model param
157. ply Now Cancel Axis Format Use these boxes to set the axis titles and how axis values are formatted Decimals refers to the number of places past the decimal to format axis values e g 3 1415 has 4 places past the decimal check exponential to format the axis value in scien tific notation e g 3 14E0 For 3 d maps boxes for the Z Axis are also provided as shown above for x y and bar graphs there will be no boxes for the Z Axis The font for axis and values can be reset with one of the Change commands 32 Chapter 2 Getting Started Graph Settings Contour Details Tab The Contour Details Settings tab of the Graph Settings Dialog Window allows you to edit map contour parameters Some of these settings are identical to those that ap pear in the Map Window and changing values here will also change values there for other maps e g Anisotropic Surface Maps this window is the only place where con tour details can be set Graph Settings General Axis Scaling Axis Ties Labels Contour Details 3D Proportion Legend os V Show legend oj c Pose Height Width Continuous d 2 4 C Stepped Map Surface Contour lines Solid pedestal Map Ceiling Map Floor Contour lines Color band Contour lines v Colorbands 7 wireframe r M Smoothing Weave Contour Levels Color Grid Lines
158. pter 14 Mapping Map Image 2 d The 2 d map image is produced when the Graph Type is set to 2 d 01 Mouse Action 80 0 Off m Reset 0 733 0 653 Mouse Location 85 ies X718 Lys Y 45 5 0 533 a 0 493 Z 0 514 m north Map Image 2 d Standard Deviations A 2 d map of standard deviations can be created from the Map Window Map Image Pb SD lO xl Mouse Action 80 0 Off Y Pb SD 0 141 Mouse Location 0 85 X 426 0 130 65 1 0 125 EE 0 119 Z 0 096 m north 155 Chapter 14 Mapping Map Image 2 d Sample Posting The 2 d sample posting is produced by the Draw command from the Mapping win dow when the Graph Type within that window is set to 2 d and the Posting box is checked Each X symbol in the image below marks an actual sample location as defined by the original X Y coordinate locations in the Data Worksheet window Co ordinate Postings Quantile Plots of the active data which may or may not be the same as the mapped data are viewed through the Data Summary X Y Coordi nates Tab window described earlier 5 Mouse Action Off m 0 653 Mouse Location UIT X724 0 573 E t 0 533 deny 2 0 493 Z 0 671 E Commands in this Window are the same as for earlier graphs 156 Chapter 14 Mapping Transects 1 d Maps The 1 d transect image with or without sample postings is produced v
159. purchase price or b replacement of the software that does not meet Gamma Design Software s limited warranty In either case software must be returned to Gamma Design Software with a copy of the sales receipt This warranty is void if failure has resulted from accident abuse or misapplication Any replacement will be warranted for one year 2 The warranties and remedies set forth above are exclusive and in lieu of all others oral or written express or implied No Gamma Design Software distributor or em ployee is authorized to make any modification or addition to this warranty U S Government Restricted Rights GS software and documentation are provided with RESTRICTED AND LIMITED RIGHTS Use duplication or disclosure by the Government is subject to restrictions as noted in sub paragraph c 1 ii of The Rights in Technical Data and Computer Software clause at 52 227 7013 The manufacturer is Gamma Design Software P O Box 201 Plainwell MI 49080 General You must register your copy of GS to be eligible for customer support and service You may 13 Chapter 2 Getting Started do so on line at www gammadesign com or during the installation process If you have ques tions about this agreement write to Gamma Design Software P O Box 201 Plainwell MI 49080 U S A 14 Chapter 2 Getting Started Chapter 2 Getting Started From Data to Maps How to Proceed To make a map using GS First collect samples from kno
160. r a discrete area around an interpolation point Punctual or point kriging provides an estimate for a precise point In environmental work block kriging is usually more appropriate The block is defined as the rectan gular area around a point that is not included in an adjacent block Brackets as Column Title Separators Column or variate names are separated by brackets e g m east m north Pb ug g pH C or Structural Variance C of the variogram model represents spatially structured variance Compare to Co or nugget variance which is the portion of the variance not spatially structured Cy or Nugget Variance Co or Nugget Variance is the y intercept of the variogram model Nugget variance represents variation not spatially dependent over the range examined Characters as Column Title Separators Column or variate names are separated by a character specified in the field that ap pears when this option is selected For example if were specified as the separat ed m east m north Pb ug g pH Character Separated Values Values within data records are separated by a specific character defined in the field below the list box e g if the character is the delimiter 13 2 34 5 35 6 0 15 Cokriging An interpolation technique that allows one to use a more intensely sampled covari ate in the estimation of values for a related variate If the primary variate is difficult 162 Chapter 16 Glossary
161. r an easier to measure related covari ate and Inverse distance weighting provides simple nearest neighbor interpolation based only on distance to nearby samples GS provides basic parametric statistics Sample means and variance Frequency distributions probability distributions and skewness and kurtosis measures for determining departures from normality and Quantile plots or coordinate maps show the distribution of sample values across the spatial domain Transformations for returning the data to normality and Regression analysis for covariates vs primary variates System Requirements GS requires a Windows based PC running Windows XP or later Installation To install GS 1 If GS is on a removable media such as a CD insert the media into your drive and the install process should start automatically if it does not go to the drive for the media and double click on SetupGSWint10 exe 2 If you have downloaded GS then go to the folder into which you placed your download file and double click on SetupGSWin10 exe 3 The setup program will prompt you through the installation process Follow the instructions on the screen You will be prompted for a serial number and a license or activation code These numbers can be found on the CD pack age or in your download confirmation email Note You may be required to run the setup program as an administrator If so right click on SetupGSWin10 exe and choose Run as adminis
162. rds 1 8 25 and 26 have identical coordinates How do you want to handle Use first value make other values missing Use average value make none missing C Use last value make other values missing Use sum of values make none missing Stop data build and examine worksheet Cancel IV Also take this action for other duplicates of this build Use first value make other values missing This option includes the first record encountered record 1 in the case described in the analysis and marks other duplicates in the worksheet records 8 25 and 26 as temporarily missing values So long as these values remain marked as missing on subsequent worksheet rebuilds this Duplicate Query warning will not occur Use last value make other values missing This option is the same as the first option above except that the last record encoun tered is used in the analysis record 26 in the case described rather than the first Use average value make none missing This option directs GS to use the average of the duplicate records It does not mark any values in the worksheet missing which means that the next time the work sheet is rebuilt this Duplicate Query warning will occur again Stop data build and examine worksheet Specifying this option will cause the data build to halt and will display the first dupli cate record of the data worksheet Any other duplicates already found during the data build will be reset to non missing w
163. rea of the worksheet contain data for each variate To enter or edit data in any given cell double click on that cell To enter a formula rather than a value amp o begin the cell with an sign The data worksheet has a capacity for 2 billion records and up to 64 columns To sort the datasheet click on the topmost row of the column Sorts will alternate between ascending and descending order Or use the Sort command in the Data Menu To change the number of decimal places to show for any given column use the Decrease Decimals or Increase Decimals command in the Data Menu or click on the respective tool icon in the menu bar If in the Preferences Window you have specified an automatic format for decimals to report changing the number of deci mal places for the X Y or Z columns will change the number of decimal places used in subsequent worksheets and graphs To change the width of any column move the cursor to the top of the column and use the mouse to stretch or contract the column margins To temporarily delete a cell from analyses change it to a Temporary Missing Val ue with a click of the right mouse button its color turns red and the font becomes italicized see the value 0 37 in the diagram above Another right click restores it to the worksheet its color will return to black and font to normal To change a value to a Permanent Missing Value delete its contents by highlight ing it and pressing the Delete key
164. related and the variogram reaches an asymptote The formula used for this model is y h Co C 1 5 h A 0 5 h A forh A 88 Chapter 6 Semivariance Analysis Overview y h Co C forh A where y h semivariance for interval distance class h h lag interval nugget variance gt 0 C structural variance gt Co and A V Aj 0 AZ A range parameter for the major axis 0 In the case of the spherical model the range or effective range for the major axis Aj A range parameter for the minor axis 90 In the case of the spherical model the range or effective range for the minor axis Ao angle of maximum variation angle between pairs Exponential Anisotropic Model The exponential anisotropic model is similar to the spherical in that it approach es the sill gradually but different from the spherical in the rate at which the sill is approached and in the fact that the model and the sill never actually converge The formula used for this model is y h Co exp h A where y h semivariance for interval distance class h h lag interval Co nugget variance gt 0 C structural variance gt Co and 0 AZ sin 1 range parameter for the major axis In the case of the exponential model the range or effective range for the major axis A
165. ress Cancel to close the window without saving changes Defining a Regular Interpolation Grid With the Regular Interpolation Grid dialog window you may define the region to be kriged or interpolated as well as the intensity at which the interpolation is to take place This method for specifying interpolate locations is appropriate for interpola tions at regular intervals across an area if the interpolations are to be performed at odd locations use the Irregular x y Interpolation Grid If the outline of the area is a complex polygon you should still use this dialog Regular Interpolation grid but then specify the shape of the polygon from the Interpolation window see Polygons be low Note that for 1 dimensional data sets e g transects or time series only the X direction is displayed in the dialog window 121 Chapter 9 Interpolation Basics Uniform Interpolation Grid x Distance Number interpolation Range Interval of points Data Range X 0 00 80 00 1 0000 81 0 60 79 30 Y 0 00 80 00 1 0000 81 1 50 79 00 _Optimize _ Reset Cancel Interpolation Range Specify the beginning and ending values for the region to be interpolated The re gion may exceed the data range which is noted on the right side of the dialog win dow Irregularly shaped areas within the bounds of the interpolation range may be interpolated by specifying polygon masks from the Krig window The number of decimal places used to define the r
166. riate Records 6 contain the 2 values organized in row order Within each row the y coordinate is constant and the grid row 1 corresponds to the lowest y coordinate value and the last row corresponds to the highest y coordinate Within each row the z variate values are ordered from low x coordinate to highest x coordinate DSAA 376 253 185556 375 194194 225 127261 523 128262 152 81 000 4469 000 578 746 1097 1251 581 312 229 229 235 278 292 357 490 997 1411 1397 1373 1373 1370 1061 942 1003 1288 1014 785 963 934 797 703 924 1035 1071 1257 1775 1800 1520 1460 1520 1278 1098 915 645 495 450 378 339 342 425 613 1084 1292 1701 1682 1996 2280 2107 1662 1553 1418 1162 1225 1266 1735 1674 1550 1800 2015 2240 2158 2328 2262 2173 2046 1688 1849 1880 2023 2320 2029 2140 2240 2650 2465 2369 2180 Chapter 13 Interpolation Output File Formats GSLib Output out Format The GSLib out interpolation output format has a short header area that provides information for mapping The first header record shown on 2 lines below because of page width limitations contains x and y coordinate information needed for mapping The second record states the number of fields per data record and the next records contain the names of the fields Following the header records are records that con tain a value for the Z estimate and the estimation variance for that point or estima tion standard deviation if specified in the Interpolation Window Data records beg
167. rid specified points An irregular grid is composed solely of interpolation locations specified by the user Press Define to bring up an Interpolate Worksheet within which locations can be defined or imported from an external text file Include shapes polygons Specific shapes can be interpolated or excluded from being interpolated by de fining inclusive or exclusive polygons prior to kriging Press Define to bring up a Polygon Outlines Worksheet within which to define polygons See Define Poly gon Outlines later in this chapter Ininclusive polygons the area within the polygon is interpolated or mapped In exclusive polygons the area within the polygon is not interpo lated or mapped Constrain Z estimates The estimated Z values interpolates can be constrained to a specific range For example if values less than zero are inappropriate you can specify that Z estimates less than zero be reported as zero Press Define to bring up a dialog box to specify Z Estimate Boundaries described later in this chapter Output File Name Press Select to select an existing or new file to which kriging interpolation estimates will be written To examine the contents of an existing file press View Output Format The format with which GS will write estimates to the file can be one of several types 118 Chapter 9 Interpolation Basics GS format krg in this format a header area defines the interpolation grid varia
168. rint dialog will appear Graphs can be copied to the Windows clipboard via the menu command Edit Copy or the control C shortcut The window containing the graph must be active select ed prior to pressing the Copy command in order for the graph to be copied You can also Copy graphs by right clicking on the graph to bring up a context menu Graphs can be exported as graphic files via the menu command File Export Graph You have the option of saving graphs as enhanced metafiles emf standard Win dows metafiles wmf bitmap files bmf PNG files png or jpeg files jpg You can also export graphs by right clicking on a graph to access an Export command Printing Copying and Exporting Worksheet Data Worksheet data can be printed copied to the Windows clipboard and exported to an external file in the same way that graphs can be Right click on a worksheet to bring up a context menu with these commands exposed These tasks can also be performed via the main menu printing can be performed through the File Print menu copying can be performed through the Edit Copy menu and exporting can be performed through the Data Export menu so long as the currently selected or active window contains a worksheet If a block of cells is highlighted when printing copying and exporting is invoked only that block will be acted upon Available export formats include text files with either tab separated values txt or comma separated
169. rting data files to indi cate that a value is missing Missing values are ignored during data builds and sub sequent analyses This value can be overridden by values specified in individual dialog windows Window background color Change the background color of the main GS window The default color is the color of your desktop Click on the color panel to change the color Default graph background color Change the default Graph background color by clicking on the color panel Default values can be overridden for individual graphs using the Graph Settings dialog Show tips Display short explanations of commands and input boxes when mouse hovers over buttons and boxes Put Z Name in Window Title Puts the name of the Z variate in the title bar of specific windows Show all warnings Display warning messages even though you may have earlier elected to turn off warnings on some warning dialog screens where there is a Do not show this mes sage again check box when you choose to Show all warnings these messages are again shown Places Past Decimal For different types of variates allow GS to format values automatically or specify the exact number of places past the decimal to report in windows and printouts All calculations are performed on double precision values regardless of the values re quested here These default values can be overridden by values on specific dialog windows such as the Field Assignment Dialog of the Data Worksheet
170. s formed data as below If the data are not transformed only the left hand graph will appear Data can be transformed in the in the Data Summary window The number of frequency classes bars can be changed using the Edit Graph command In addition to a frequency distribution bar graph you may also choose to view a Cumulative Frequency Distribution or a Normal Probability curve described below Frequency Distribution Pb nl NonTransformed Transformed Frequency Frequency 0 2 813 1 801 0 789 0 223 In Pb Plot Frequency hf 56 Chapter 5 Summary Statistics Plot Type of plot to graph Choose either Frequency as displayed above Cumulative Frequency or Normal Probability curves shown later Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu Frequency Distribution Values The Frequency Listing window provides a listing of the values used to create the frequency distribution graph The number of classes is set from Frequency Distribu tion window using the Edit Graph command This is a read only worksheet ac cessed with the List values command from the right click menu or the Data List graph values command from the GS main command menu Frequency Distribution Values Pb lol Class Pb Midpoint Frequency 1 0 06 2 2 0 12 9 3 0 19 18 E 0 25 18 5 0 31 18 6 0 37 10 7 0
171. s the Offset Tolerance determines how closely the alignment between any two points needs to be for those points to be included in the analysis for a given offset angle Two points will be included in the analysis for a given offset angle if the angle between them is within the offset tolerance from the offset angle For example if the angle between two points is 59 3 and the offset tolerance is 73 Chapter 6 Semivariance Analysis Overview 15 02 the points will be included only in the 45 angle class which would include all angles between 30 and 60 The default tolerance is 22 52 Variogram Options Show Sample Variance Check this option to show the sample variance for the data as a dashed line on the variogram graphs Show Variogram Model Check this option to show a model for the variogram points If the model has al ready been defined either automatically or manually the variograms will be redrawn with the model now graphed If a model has not yet been defined or upon execut ing the Calculate command a best fit model will be calculated and graphed To see the model parameters and to change the model use the Model command at the bottom of the variogram image Expand The Expand command brings up a separate variogram window from which the variogram can be printed or formatted Variance Cloud Analysis the ability to view individual semivariance values and the number of pairs per variogram class interval are also av
172. s that has been specified the missing value indicator and thus the third val ue of this record will be read into the worksheet as a missing value 13 2 34 5 0 15 Autocorrelation Autocorrelation is the degree to which a property is related to itself in time or space For example in a spatial domain values for samples taken close to one another are more likely to be similar than are samples taken farther apart autocorrelation is a formal measure of this self similarity Backtransformation When data values are transformed in order to make their distributions more normally distributed after analysis of the transformed data the output data are customarily but not necessarily back transformed to the original data domain for final reporting For example the backtransformation for a In z transform is exp z transformed for a 2 transform the backtransformation is the square root of the transformed value 161 Chapter 16 Glossary Offset values if applied are subtracted from the backtransformed values Binary Data Record Format Binary data from many spreadsheet and database programs can be imported direct ly Eligible files include Excel and Lotus 1 2 3 worksheets dBase Paradox Access and FoxPro Block Kriging Kriging provides a means of interpolating values for points not physically sampled using knowledge about the underlying spatial relationships in a data set to do so Block kriging provides an estimate fo
173. s used to import text files as described earlier When importing spreadsheets the first row of the imported spreadsheet should hold the variate names that appear the GS column headings Day in column 1 be low If the first row of the spreadsheet contains values they will be ignored Import Excel Spreadsheet 10 x File name GAGSWin 32 Version 9 Working files Cokrig xis Cancel Worksheets Available Column Assignments Demo 1d Properties ID 1 X 2 Y 3 Z4 _ Change 2 3 Date mean daily C 890101 00 3 830103 00 5 60 9 10 890105 00 4 30 10 20 890106 00 0 60 2 10 890110 00 1 70 5 90 890111 00 2 30 6 70 830112 00 1 00 4 00 830114 00 4 00 4 7 20 890115 00 0 00 2 50 890117 00 00 030 gt daily daily min D 6 10 Worksheets Available The worksheets or tables within individual spreadsheet or database files are listed here and can be chosen via the pull down listing Properties The Properties Command brings up a File Import Properties dialog window within which you can specify how GS should identify missing values When importing spreadsheets and databases other file import properties are limited to single pre defined choices e g spreadsheet columns are used to denote different GS Work sheet fields Change Column Assignments The Change command brings up a Field or Column Assignment window from which you can assign variates e g X coordinate to columns or f
174. sadvantage is that if there are few pairs of points for the shortest distance classes when the first lag is not offset a common problem there will be even fewer pairs available with the first lag offset If this is the case there will be little if any improvement to the variogram For individually specified lag class intervals pairs of points are assigned to interval 70 Chapter 6 Semivariance Analysis Overview lag classes based on values in the Define Lag Class Intervals window GS calculates a semivariance statistic for each interval class the graph of all h s vs all semivariances for each interval class in the analysis constitutes the variogram more properly called the semivariogram For cokriging semivariance analysis must be performed for the primary variate Z for the covariate Z2 and for the cross variate Z x Z2 situation Autocorrelation Window The Autocorrelation Window is where various options for variogram calculations and the end results appear see the Semivariance Analysis summary for a definition of semivariance and formulas for lag class distance intervals Autocorrelation Analysis Primary Variate Ur xj Active Lag Distance 80 00 E Anisotropic Axis Orientation exe Variogram Options Lag Class Distance Interval Principal Axis degrees N 0 Show sample variance Uniform interval 800 zl 22 50 cd Offset tolerance degrees 22 20 71 V Show variogram model
175. se the Data Change Decimals menu commana Clicking on the top of a column will Sort the worksheet based on the column select ed in alternating ascending or descending order You may also change Column Widths by placing the cursor over the line between two columns and dragging to a new location Normal Probability Distribution The Normal Probability Distribution window contains a normal probability curve for the Z variate If the data are transformed two graphs will appear with the distribu tion for the transformed data to the right of the distribution for the nontransformed data as below If the data are not transformed only the left hand graph will ap pear Transformations are performed in the Data Summary window The normal probability curve is the same as a Cumulative Frequency distribution with the y axis logn transformed If the data are normally distributed the curve will describe a straight line E G in the graph below transforming the data acts to nor malize the distribution 59 Chapter 5 Summary Statistics Normal Probabiliby Distribution Pb inet x NonTransformed Transformed 46 om et 3 4 22 F e 0 In Cumulatiwe Pct In Cumulative Pct 5 to 2 813 1 801 0 789 0 223 Pb In Pb Plot Normal Probability Plot Type of plot to graph Choose either Frequency Cumulative Frequency or Normal Probability as displayed above curves Actions Y
176. sion is available you will be asked if you would like to connect to the proper web page for an update For this feature to work your computer must have access to the internet Communication is conducted using your browser You can also check the GS update status manually by checking your program s version available from the About GS screen against the version displayed at www gammadesign com Email Gamma Design send an email message to sup porto GammabDesign com using your default email program For this feature to Work you must have access to the internet and a default email program in stalled Go to www gammadesign com connect to Gamma Design s home page through your normal internet provider using your default browser Register On line open a registration page to register with to Gamma Design Software Deactivate transfer your GS license to the activation server After transferring your license you will not be able to open GS again until it is reactivated on this or another computer You must be connected the internet in order to deactivate About GS display title and copyright screen and also display the current GS version number Chapter 2 Getting Started Right Click Context Menus When you right click over a graph or worksheet a context menu will appear that will allow you to edit print export or list the values in a graph or print or export work sheet values Cut Copy Paste and Del
177. ssing x y or z value or because they were excluded from the analysis by the Filter command 4 values in the example above If duplicate values were averaged see the Duplicate Values dialog then all the duplicates for a given location count as a single record and the duplicates will not be counted as missing 55 Chapter 5 Summary Statistics Numbers in parentheses following skewness and kurtosis are standard errors of these terms When analyzing data sets with a covariate Z2 present the following rules apply Q Only records with a valid Z and a valid Z2 value will be included in the anal ysis of Z Allrecords with a valid Z2 value will be included in the analysis of Z2 This is because covariance analysis expects all sample points for Z to be accompa nied by a covariate Z2 which will also be sampled at places other than where Z is sampled The summary statistics and autocorrelation analysis for Z will thus be per formed only for those values of Z accompanied by a Z2 The summary statistics and autocorrelation analysis for Z2 on the other hand will be performed for all values of Z2 regardless of whether a matching Z value is present Frequency Distribution Histogram The Frequency Distribution window contains a bar graph of the frequency distribu tion for the Z variate If the data are transformed two graphs will appear with the distribution for the transformed data to the right of the distribution for the nontran
178. stallation ID to receive an unlocking code 4 enter the unlocking code below and press Continue Use unlocking code Unlocking code Get now Installation ID 674163692444 Back _ Continue Use unlocking code Check this box to use an unlocking code to activate your copy of GS This is nec essary if you cannot access the internet from this computer In this case 1 goto another computer and open a web browser to the address www internetactivation com 2 enter your license number activation code and the 12 digit Installation ID printed at the bottom of the dialog window the Installation ID is differ ent for every computer Receive an unlocking code 3 enter the unlocking code in the window below Unlocking code Enter the unlocking code provided by the web site Get now Launch a web browser pointed to www internetactivation com Copy Copy the Installation ID to the Windows clipboard This makes it easy to transfer into the browser window with an Edit Paste command 10 Chapter 2 Getting Started Continue Return to the Activation Window In the Activation Window you must still enter your License number activation code even with an Unlocking code present the Unlock ing code allows GS to activate without a direct connection to the internet Deactivation You may transfer your activated GS license to another computer by first deactivat ing it on the current computer After tra
179. stance interval or lag class h another way is to draw an h Scattergram for each interval Variance clouds and h Scattergrams are measures of pairwise variance in autocor relation graphs In a variogram each point on the graph represents the average semivariance for all pairs of points in a particular lag class h Scattergrams and var iance clouds let you see the individual pairs of points that are used to calculate the average semivariance for that class Variance Clouds The formula to calculate variance for any given pair of points at locations i and j can be reduced to the mean square difference between the points 2 zi zj where Var variance for pair ij 2 measured sample value at point and 2 measured sample value at point j Any given pair i j are separated by a specific distance this distance is plotted along the x axis of the variance cloud graph All pairs on a specific graph are in the same separation distance lag class Note that a variance cloud is specific to both direction isotropic or a specific aniso tropic direction and to a particular lag class In the variogram below the cursor is on the point representing lag class 7 of the isotropic variogram which one might sus pect contains an outlier because it is so different from the other points 107 Chapter 8 Variance Clouds and h Scattergrams igi x Pb Isotropic Variogram 2 12 g 159 EETA 4 E 0 53 0 00
180. t Make the azimuth angle displayed in this window the Principal Anisotropic Axis in the Semivariance Analysis window Pressing Set will reset the Principal Anisotropic Axis for consistency the angle in the Semivariance Analysis window will display a value between 0 and 180 so that a value gt 180 will appear as that value less 180 e g 225 will be reset to 90 in the Semivariance Analysis window Set will force a Rebuild of the anisotropic variograms and models if selected in the semivariance window The Principal Anisotropic Axis the Major Axis of the aniso tropic model should be the direction of major spatial continuity or major axis of the anisotropic variogram model corresponding to the direction with the longest range Correspondingly A should be smaller in the major direction lower average semivar iance and largest in the minor 90 offset direction A The average semivariance for the azimuth transect is displayed as A nnn beneath the Set command where nnn is the average semivariance A should be smaller in the major direction lower average semivariance and largest in the minor 90 offset direction Mouse Action Off returns the mouse to normal operation Rotate turns the cursor into a rotator cuff when the left mouse button is pushed allowing the image to be rotated as desired This option is available on ly for 3 d map projections Move allows the graph to be moved within the window by clic
181. t x axis e Y axis place a vertical grid line along the back wall of the 3 d plot y axis e Z axis place horizontal grid lines along the back walls of 3 d plots Draw Create the map in a Map Image window 149 Chapter 14 Mapping Map Contour Intervals This dialog window allows one to specify the break points and colors for the contour intervals used for mapping The number of contour intervals is specified in the Map window where access to this Map Contour Levels window is provided 10 Map Contour Levels r Contour Intervals p 787 Cancel Exit 15 0 745 Intervals Reset u E m END Get Save 13 Include colors V 0 660 n 0 618 Color Source 11 Standard Red 0 575 C Bue Green C Custom Gray Dynamic invert 0 364 To change colors click on m colored tab next to interval Contour Intervals e Color buttons change the color of a specified interval by clicking the adja cent color button e Break points change the break point between adjacent contour intervals by providing a new value in the space provided Note that the new break point must be greater than the preceding point and less than the one that follows e Missing value specify the missing value indicator for the data file This val ue is usually embedded in the input file as part of the header information and 150 Chapter 14 Mapping is automatically extracted by GS
182. tab to brings up the Madograms window 815 Pb Isotropic Madogram Semivariance M 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90Degr amp lt gt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other commands work here as they do for the Variograms Window 97 Chapter 7 Other Autocorrelation Measures Rodograms Rodograms are similar to traditional variograms see Semivariance Analysis except that the square root of the difference between 2 and 2 15 calculated rather than the square of the difference The formula thus becomes yR 1 2N h DEM zi Ziel 1 where yR h semivariance R for interval distance class h 2 measured sample value at point Zi measured sample value at point h and N h total number of sample couples for the lag interval h Rodograms both isotropic and anisotropic appear in the Autocorrelation Window on the Rodogram tab Press the Expand button on this to tab bring up the Rodo grams window Rodograms Pb nl x Pb Isotropic Rodogram 0 787 oOo goo B Bg 0590 O o o 5 0394 2 0 197 0 000 0 00 26 67 53 33 80 00 Separation Distance h Isotropic 45 Degrees 90 Degra gt Scatter Right click to edit list print etc or click point for variance cloud The Cloud Scatter right click menu and other comman
183. te names and other information about the file needed to initiate mapping later and the data records include for each X and Y Coordinate location that is kriged the interpolation or Z estimate the standard deviation of the Z estimate and the number of neighbors that were used to make the estimate See de tailed example below Surfer Grid format grd in this format a short header area defines infor mation needed for mapping and the data is written as a continuous stream of Z estimates beginning from the NW corner of the interpolation grid The stand ard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format This format is compatible with Golden Soft ware s Surfer mapping program Note that this format is not the same as the Surfer XYZ Input file format See detailed example below ArcView Format asc this is similar to the Surfer format but the header area is formatted differently and the Z estimates are written in a pattern that begins from the NW corner of the interpolation grid The standard deviation of the esti mate and the number of neighbors used for interpolation are not included in this format Also for this format the x and y interpolation intervals must be the same you can set them to be the same from the Interpolation Grid dialog win dow This format is compatible with ESRI s Arcinfo Geographic Information System See detailed example below GSLib Format o
184. the Z variate If you choose a column that is already assigned the other variate s column will switch with the original Z column Z2 Covariate the specified column contains values for the Covariate The Covariate is used in cokriging If you choose a column that is already assigned to another variate the other variate s column will switch with the original Z2 col umn External Drift the specified column contains the external drift data If you choose a column that is already assigned to another variate the other variate s column will switch with the original external drift column Rebuild automatically when reassign Rebuild the internal worksheet when window closes This is equivalent to pressing the Rebuild button on the Data Worksheet window 40 Chapter 3 Working with Data Covariate Values Warning In cokriging there are usually more Z2 covariate values than primary Z values If your column field assignments for Z and Z2 result in data arrays with more Z val ues than Z2 values then you will get the warning notice below You may continue the analysis with more Z than Z2 values but there is no ad vantage to doing so in cokriging Z values without corresponding Z2 values are treated as missing Likewise there is no advantage to cokriging when you have just as many Z2 covariate values as you have Z values 65 Alert x Warming There are fewer covariate Z2 values than there are primary 2 values Usually
185. trator For some configurations it may also be necessary to right click the Properties menu and on the Compatibility tab choose Run this program in Compatibility mode for Windows XP Service Pack 3 Chapter 2 Getting Started Activation GS requires activation prior to first use once the evaluation period has expired Ac tivation is performed over the internet and requires a unique license code for each installation of GS Activation must be performed within several days of first installa tion the activation screen provides the number of days remaining If you have already downloaded and installed an evaluation version of GS you do not need to reinstall GS once you have purchased a license Instead choose Acti vate GS now from the start up activation window see below If you do not activate GS within the time period specified by the activation screen GS will stop working You may activate after this point without having to re install the program If the computer on which you want to activate GS is not connected to the internet you may get a special unlocking code by logging into the activation server from a computer that is connected to the internet See Advanced Options below for how to do this The license code required for activation is either on the CD sleeve or in the pur chase confirmation email that you received Activation node locks GS to a specific computer Once your copy of GS has been activated
186. u are editing a bar graph an x y scatter graph e g a variogram or a 2 d or 3 d map In the case of a 3 d map for exam ple there will be a place for scaling and renaming the Z axis in addition to the X and Y axes In addition to the General tab there is also a tab for Axis Scaling Axis Ti tles and Labels and Contour Details only available for maps Graph Settings General Axis Scaling Axis Ties Labels Contour Detais Graph Colors Borders Lines sane Text Quartiles Plot Exterior Font Plot Interior M Box in ize Legend Interior _ Defaut Style Normal Change Graph Title Graph Footnote Text Text Font Font Name Arial Name Arial Size 8 Size 8 Style Normal Style Normal Graph Colors Tab You may set background colors for three different parts of the graph Click on the color bar to the right of the component name to bring up a Color Dialog Window that will allow you to change the color of that component the color of the bar indicates the current color Graph Borders Tab You may set border styles for the graph and for the legend if shown Width refers to the width of the border and Print allows you to choose to print or not print the bor der when printing 29 Chapter 2 Getting Started Graph Colors Lines Width Print Type Graph None 1 Legend Etcned out 1 7 Lines Tab On graphs with lines
187. uild The Rebuild command builds the data arrays on which all geostatistical analyses are based This command is enabled whenever data records have been edited The data arrays must be rebuilt prior to semivariance or other analysis whenever data have been changed Sometimes this occurs automatically such as when col umns are reassigned Other times such as when individual cells are edited you must rebuild the data arrays yourself by clicking on this button When rebuilding is needed the Rebuild command will become enabled and the color of the font will change to red During rebuilding the data are checked for duplicate coordinate loca tions and for a sufficient number of valid records Note that rebuilding is only needed when column assignments change or when data within a column assigned to a coordinate or z variate changes In the screen above changing a value within the Al column will not require arrays to be rebuilt because no analysis variates X coord Y coord Z or ID are assigned to the Al column Filter Press Filter to bring up a Filter Dialog that allows the data to be constrained to a particular range data outside of the specified range are treated as temporary miss ing data i e excluded from subsequent analyses The filter check box turns filtering on and off Clear Press Clear to empty the data worksheet and reset all analysis windows Has the same effect as the File New menu command Data Title Description Any t
188. urfer X Z x ote ra ra a ETA 49 Spreadsheet and Database Input 50 Input File Formats File Import Properties 51 Table of Contents Viewing Files File View Window eH Appending Data to an Existing Worksheet Data Append Dialog Chapter 5 Summary Statistics 2 re oett ee edit Frequency Distributions Frequency Distribution Histograms amp Values Cumulative Frequency Distribution amp Values Normal Probability Distribution amp Values X Y Coordinates Summary sse Coordinate Postings Quantile Plots 2 Dimensional Data 1 Dimensional Data Defining Posting Regression Analysis Cross Variate Regression Regression Chapter 6 Semivariance Analysis ONVGIVIQW icis lee Eidem gu aes fiae bte The Autocorrelation Window seseeeeneenneennen Define Irregular Lag Class
189. ut this format is similar to the GeoEas input format A long first record contains coordinate interval information that is read by GS when mapping GSLib files The second record of the file specifies three header rec ords named estimate estimation variance or standard deviation and neighbors Records that follow in the same order as for Surfer but there are three fields per record estimate estimation error and number of neighbors rather than just one field the Z estimate See detailed example below Output Variance You may choose to report estimation error as estimation variance or as estimation standard deviation Search Neighborhood GS interpolates values for a specific location using nearest neighbor values weighted by distance Only a certain number of near neighbors are used to calculate the interpolation estimate and neighbors can be required to be within a particular geographic area around the location being estimated The default value of 16 nearest neighbors is usually sufficient and also by default no 119 Chapter 9 Interpolation Basics restrictions are placed on the neighborhood radius in Kriging neighbors outside of the variogram range are weighted identically and if significant structural depend ence is present weighted minimally Specifying more than 16 neighbors can slow interpolation substantially although up to 64 neighbors are allowed The geographic area to be searched can
190. vaerts 1997 page 98 A map will appear incomplete checkered cells as below when there are not at least 3 pairs of points to provide an average semivariance for a particular lag class and direction Cells with fewer than 3 pairs will appear to be missing Cell size is de pendent on the lag class distance interval Anisotropic Variogram Map Pb gt inl B x 34 80 00 M Azimuth 48 231 348 i Semivariance a 1 382 gt 26 67 1289 Set o 1 207 1114 A 0 27476 M 1 021 m 0 928 Mouse Action a 0 825 0 743 Off yi 0 650 0 557 Reset amp 26 67 0 484 o 0 371 ii m Mouse Location 0 188 il ux X 39 14 9200 Y 33 23 Z 0 559 80 00 80 00 26 67 26 67 80 00 Separation Distance E W Actions You may Print Copy Edit Export or List graph values for either graph using the menu commands of the main GS window or via a right click menu 3 d Change the graph projection to 3 d from 2 d or to 2 d from 3 d Chapter 6 Semivariance Analysis Overview Azimuth When the check box is marked a transect on the map surface illustrates the azimuth angle The angle is specified in the text box e g 348 in the window above and also displayed graphically in the area under the azimuth angle The average semi variance for the transect is displayed as A nnn beneath the Set command Note that there is no difference between an angle and that angle plus 180 Se
191. verse Distance Weighting IDW and Normal Distance Weighting NDW in which interpolation estimates are made based on values at nearby locations weighted only by distance from the interpolation location Neither IDW nor NDW make assumptions about spatial relationships except the basic assumption that nearby points ought to be more closely related than distant points to the value at the interpolate location IDW applies stronger weights to nearby points than does NDW All of these techniques are described in greater detail on the following pages 116 Chapter 9 Interpolation Basics The Interpolation Window The Interpolation Window provides access to Kriging Cokriging Conditional Simula tion and Inverse Distance Weighting techniques for estimating values for points not sampled Interpolation produces an output file that is used by GS for mapping The output file can also be read by other mapping programs Interpolation Pb xj Interval Points n X 0 00 80 00 1 00 81 Y 0 00 80 00 1 00 81 C Irregular x y grid include shapes polygons Define Constrain Z estimates Define Calculate Validation Cross validate C Jacknife Define Validate Output File Krig simulate ow CADocuments and Settings Demo krg Kriging Type Browse Ordinary cs Gria cro zi TESA I External Drift Define Output Variance Polynomial Tre
192. which can be described based on three parameters Nugget Variance or Co the y intercept of the model Sill or the model asymptote Range or A the separation distance over which spatial dependence is appar ent Sometimes this is called the effective range in order to distinguish range A from a model s range parameter In GS the Range A is calculated from A as described in the formulas for the different models later in this chap ter Generalized Variogram Model Semivariance 0 20 40 60 80 Separation Distance h 79 Chapter 6 Semivariance Analysis Overview GS calculates default values for each parameter of the five models You may change any of these three model parameters from the Isotropic Variogram Model dialog window Isotropic Variogram Model q xj Variogram Nugget Structural Variance Model Type Variance Co Sill Co C Range Spherical 0 123700 0 350400 59 2000 LEE mu bes This Fit r AutoFit Residual SS 2 973E 03 2 973E 03 r2 0 940 0 940 Proportion C Co C 0 647 0 647 Model Spherical Spherical Autofit Cancel Variogram Model Type Choose one of four isotropic models Linear Spherical Exponential and Gaussian As a model is chosen the variogram graphs will be updated to denote the change Model Terms Any of the three model parameters for each model may be changed within the rang es allowed for individual parameters To change a va
193. wn locations The sample locations do not need to be evenly spaced or even to lie on a grid you simply need to know their location in a Cartesian x y coordinate system Note that latitude and longitude are not Cartesian coordinates if your data are in latitude longitude coordinates you should first convert them to Cartesian units such as UTM there are many calculators for doing this on the web Second bring the data into the GS Data Worksheet you can enter the data directly into the worksheet or import the data from a text file spreadsheet or another source often the easiest way to import data is to cut and paste from the source spreadsheet or text file Third perform Semivariance Analysis to produce a variogram model of the autocorrelation present in the data Fourth use Kriging Cokriging or Conditional Simulation to produce an inter polation file that will contain optimal estimates of values at evenly spaced in tervals over the sample area alternatively you can use Inverse Distance Weighting IDW but your interpolations will not be optimal and Finally draw a 3 d or 2 d Map of the property This map will be an optimal unbiased representation of the property over the area of interest You can also produce a confidence map for the estimates which will allow you to as sess the statistical error associated with each estimated contour interval General Screen Layout The main GS window has a command menu at the top and ho

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