>A 600/8-91/008
united States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
P.O. Box 93478
Las Vegas NV 89193-3478
EPA 600/8-91/008
April 1991
Research and Development
vvEPA GEO-EAS 1.2.1
User's Guide
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EPA 600/8-91/008
APRIL 1991
GEO-EAS 1.2.1
GEOSTATISTICAL ENVIRONMENTAL
ASSESSMENT SOFTWARE
USER'S GUIDE
by
Evan Englund
U.S. Environmental Protection Agency
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89193-3478
Allen Sparks
Computer Sciences Corporation
4220 S. Maryland Parkway
La Plaza B, Suite 408
Las Vegas, Nevada 89119
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89119
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NOTICE
The information in this document has been funded wholly or in part by the United States Environmental Protection Agency under
Contract #68-01-7325 to Computer Sciences Corporation. It has been subjected to the Agency's peer and administrative review,
and it has been approved for publication as an EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
DISCLAIMER
Geo^EAS software and documentation are provided "as is" without guarantee or warranty of any kind, expressed or implied. The
Environmental Monitoring Systems Laboratory, U. S. Environmental Protection Agency, Las Vegas, NV, and Computer Sciences
Corporation will not be liable for any damages, losses, or claims consequent to use of this software or documentation.
ABSTRACT
This report describes how to install and use the Geo-E AS (Geostatistical Environmental Assessment Software) software package
on an IBM-PC compatible computer system. A detailed example is provided showing how to use the software to conduct a
geostatistical analysis of a data set.
Thirteen Geo-E AS programs are documented. The principal functions of the package are the production of 2-dimensional grids
and contour maps of interpolated (kriged) estimates from sample data. Other functions include data preparation, data maps,
univariate statistics, scatter plots/linear regression, and variogram computation and model fitting. Extensive use of screen graphics
such as maps, histograms, scatter plots and variograms help the user search for patterns, correlations, and problems in a data set.
Data maps, contour maps, and scatter plots can be plotted on an HP compatible pen plotter. Individual programs can be run
independently; the statistics and graphics routines may prove useful even when a full geostatistical study is not appropriate. For
ease of use, the programs are controlled interactively through screen menus, and use simple ASCII data files.
Geo-EAS 1.2.1 ii Notice/Disclaimer
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Table of Contents
ABSTRACT ii
TABLE OF CONTENTS iii
GLOSSARY v
ABBREVIATIONS vii
ACKNOWLEDGEMENTS viii
SECTION 1 - INTRODUCTION
1.1 OVERVIEW 1-1
1.2 EQUIPMENT REQUIREMENTS 1-1
1.3 GEO-EAS AVAILABILITY 1-1
1.4 USER PROFILE 1-2
SECTION 2 - SYSTEM SUMMARY
2.1 INSTALLING THE SYSTEM 2-1
2.1.1 The Distribution Diskettes 2-1
2.1.2 Hard Disk Installation 2-1
2.1.3 Using the Programs on Floppy Diskette 2-1
2.2 INITIATING THE SYSTEM 2-2
2.2.1 Using the Geo-EAS System Menu 2-2
2.2.2 Using the Programs From DOS 2-2
2.3 ANSWERS TO COMMON QUESTIONS ABOUT GEO-EAS 2-3
SECTION 3 - SYSTEM OPERATION
3.1 DATA 3-1
3.1.1 Geo-EAS Data Files 3-1
3.1.2 File Naming Conventions 3-2
3.1.3 System Defaults Option 3-2
3.2 INTERACTIVE SCREENS 3-2
3.2.1 Screen Format 3-2
3.2.2 Types of Screen Input Fields 3-3
3.2.3 The Menu Tree 3-4
3.2.4 Common Menu Options 3-4
3.3 GEO-EAS GRAPHICS 3-5
3.3.1 On-Screen Graphics 3-5
3.3.2 Metacode-Based Graphics 3-5
3.4 ERROR AND RECOVERY PROCEDURES 3-6
SECTION 4 - USING Geo-EAS IN A GEOSTATISTICAL STUDY; AN EXAMPLE
4.1 OVERVIEW 4-1
4.2 EXPLORATORY DATA ANALYSIS 4-1
4.3 VARIOGRAM ANALYSIS 4-5
4.4 KRIGING AND CONTOURING 4-13
4.5 SUMMARY AND EXERCISES 4-17
SECTION 5 -DATAPREP
5.1 WHAT DATAPREP DOES 5-1
SECTION 6 - TRANS
6.1 WHAT TRANS DOES 6-1
Geo-EAS 1.2.1 Hi Table of Contents
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TABLE OF CONTENTS (CON'T)
SECTION 7 - STAT1
7.1 WHAT STAT1 DOES 7-1
SECTION 8•SCATTER
8.1 WHAT SCATTER DOES 8-1
SECTION 9 - PREVAR
9.1 WHAT PREVAR DOES 9-1
SECTION 10 - VARIO
10.1 WHAT VARIO DOES 10-1
SECTION 11 - XVALID
11.1 WHAT XVALID DOES 11-1
SECTION 12 - KRIGE
12.1 WHAT KRIGE DOES 12-1
SECTION 13 - POSTPLOT
13.1 WHAT POSTPLOT DOES 13-1
SECTION 14 - XYGRAPH
14.1 WHAT XYGRAPH DOES 14-1
SECTION 15 - CONREC
15.1 WHAT CONREC DOES 15-1
SECTION 16 - VIEW
16.1 WHAT VIEW DOES 16-1
SECTION 17 - HPPLOT
17.1 WHAT HPPLOT DOES 17-1
APPENDICES
APPENDIX A - REFERENCES A-l
APPENDIX B - NCAR GRAPH OPTIONS B-l
APPENDIX C - HERSHY CHARACTER FONT TABLES C-l
APPENDIX D - POLYGON FILE FORMAT D-l
Geo-EAS 1.2.1 iv March 1991
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GLOSSARY OF GEOSTATISTICAL TERMS
Anisotropy
Block Kriging
Covariance
Cross Validation
Discretization
Exponential Model
Gaussian Model
Geostatistics
Inverted Covariance
(InvCov) Variogram
Kriging
Kriging Standard
Deviation
Lag
Linear Model
Madogram
In geostatistics, the situation where a variogram exhibits a longer range (i.e., better correlation)
in one direction than another.
Estimating the value of a block from a set of nearby sample values using kriging. In Geo-EAS,
the block area is approximated by a 2x2,3x3, or 4x4 array of points centered on each specified
grid node.
A statistical measure of the correlation between two variables. In geostatistics, Covariance is
usually treated as the simple inverse of the variogram, computed as the overall sample variance
minus the variogram value. These covariance values, rather than variogram values, are actually
used in the Geo-EAS kriging matrix equations for greater computational efficiency.
A technique for testing the validity of a variogram model by kriging each sampled location with
all of the other samples in the search neighborhood, and comparing the estimates with the true
sample values. Interpretation of results, however, can often be difficult. Unusually large
differences between estimated and true values may indicate the presence of "spatial outliers", or
points which do not seem to belong with their surroundings.
In kriging, the process of approximating the area of a block by a finite array of points.
A function frequently used when fitting mathematical models to experimental variograms, often
in combination with a nugget model.
A function frequently used when fitting mathematical models to experimental variograms, often
in combination with a nugget model.
A methodology for the analysis of spatially correlated data. The characteristic feature is the use
of variograms or related techniques to quantify and model the spatial correlation structure. Also
includes the various techniques such as kriging, which utilize spatial correlation models.
A variogram computed by subtracting lag covariances from the sample variance. This approach
compensates for cases where in directional variograms, the mean of the, say, west members of the
sample pairs is not the same as the mean of the east members. "InvCov" is a rather obscure term
referring to the fact that some probabilistic assumptions underlying the variogram computation
are no longer necessary. Inverted Covariance variograms may be modeled and used in kriging
in the same way as ordinary variograms.
A weighted-moving-average interpolation method where the set of weights assigned to samples
minimizes the estimation variance, which is computed as a function of the variogram model and
locations of the samples relative to each other, and to the point or block being estimated.
The standard error of estimation computed for a kriged estimate. By definition, kriging is the
weighted linear estimate with the particular set of weights which minimizes the computed
estimation variance (standard error squared). The relationship of the kriging standard deviation
to the actual error of estimation is very dependent on the variogram model used and the validity
of the underlying assumptions - therefore kriging standard deviations should be interpreted with
caution.
A distance class interval used for variogram computation.
A function frequently used when fitting mathematical models to experimental variograms, often
in combination with a nugget model.
A plot of mean absolute difference of paired sample measurements as a function of distance and
direction. Madograms are not true variograms, and generally should not be used in kriging. If
used, the kriged estimates might be "reasonable", but the kriging standard deviations will be
meaningless.
Geo-EAS 1.2.1
Glossary
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Nested Variogram
Model
Nugget Model
Octant Search
Ordinary Kriging
Point Kriging
Quadrant Search
Range
Relative Variogram
Search Neighborhood
Semi-variogram
Sill
Simple Kriging
Spherical Model
Variogram
A model which is the sum of two or more component models such as nugget, spherical, etc.
Adding a nugget component to one of the other models is the most common nested model, but
more complex combinations are occasionally used.
A constant variance model most often used in combination with one or more other functions when
fitting mathematical models to experimental variograms.
In Geo-EAS, the kriging search neighborhood ellipse may be divided into eight equal-angle
sectors, which may have minimum and maximum numbers of samples specified. A limit on the
number of consecutive empty sectors may also be specified. When the specified criteria are not
satisfied for a particular point or block then the kriged estimate is not produced.
A variety of kriging which assumes that local means are not necessarily closely related to the
population mean, and which therefore uses only the samples in the local neighborhood for the
estimate. Ordinary kriging is the most commonly used method for environmental situations.
Estimating the value of a point from a set of nearby sample values using kriging. The kriged
estimate for a point will usually be quite similar to the kriged estimate for a relatively small block
centered on the point, but the computed kriging standard deviation will be higher. When a kriged
point happens to coincide with a sampled location, the kriged estimate will equal the sample value.
In Geo-EAS, the kriging search neighborhood ellipse may be divided into four equal-angle
sectors, which may have minimum and maximum numbers of samples specified. A limit on the
number of consecutive empty sectors may also be specified. When the specified criteria are not
satisfied for a particular point or block then the kriged estimate is not produced.
For a spherical model, the distance at which the model reaches its maximum value, or sill. For
the exponential and gaussian models, which approach the sill asymptotically, Geo-EAS uses
range to mean the "practical", or "effective" range, where the function reaches approximately
95% of the maximum. The nugget model effectively has a sill with a range of zero; the linear
model uses "sill/range" merely to define the slope.
A variogram in which the ordinary variogram value for each lag has been divided by the square
of the mean of the sample values used in computing the lag. This is sometimes useful when a
"proportional effect" is present; i.e., when areas of higher than average concentration also have
higher than average variance. When relative variogram models are used in kriging, the resulting
kriging standard deviations represent decimal fractions of the estimated values.
In Geo-EAS, an elliptical area centered on a point or block being kriged. Only samples within
the ellipse will be used for kriging. When the next point is kriged, the ellipse will be re-centered,
and a different (perhaps) set of samples will be used.
Identical to the term "variogram" as defined in Geo-EAS. There is disagreement in the
geostatistical literature as to which term should be used. Geo-EAS uses "variogram" for
simplicity.
The upper limit of any variogram model which has such a limit, i.e., which tends to "level off
at large distances. In Geo-EAS, the spherical, gaussian, exponential, and nugget models have
sills. For the linear model, "sill/range" is used merely to define the slope.
A variety of kriging which assumes that local means are relatively constant and equal to the
population mean, which is well-known. The population mean is used as a factor in each local
estimate, along with the samples in the local neighborhood. This is not usually the most
appropriate method for environmental situations.
A function frequently used when fitting mathematical models to experimental variograms, often
in combination with a nugget model.
A plot of the variance (one-half the mean squared difference) of paired sample measurements as
a function of the distance (and optionally of the direction) between samples. Typically, all
possible sample pairs are examined, and grouped into classes (lags) of approximately equal
distance and direction. Variograms provide a means of quantifying the commonly observed
relationship that samples close together will tend to have more similar values than samples far
apart.
Geo-EAS 1.2.1
VI
March 1991
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ACKNOWLEDGEMENTS
This document is intended to serve both as an introduction to the Geo-E AS software package (see Geo-E AS Availability,
Section 1.3), and as a reference manual. The Geo-E AS software itself is, of course, the primary product, and deserves
a brief description of how it came about, along with an acknowledgement of the many people who contributed to its
development.
The ongoing USEPA research program in environmental geostatistics at the Environmental Monitoring Systems
Laboratory - Las Vegas (EMSL-LV) was begun about six years ago, largely through the efforts of George Flatman. As
an incidental result of various research projects conducted under Cooperative Agreements with Stanford University, the
University of Wyoming, and the University of Arizona, EMSL-LV acquired a miscelleneous collection of public domain
geostatistical and statistical software.
In the summer of 1986, as the authors were designing a relatively straightforward consolidation of this software involving
standardization of parameters and file structures, we were approached by Andre Journel and Roland Froidevaux of
Stanford, who enthusiastically demonstrated a prototype of a 'user friendly' PC-based geostatistical package written by
Froidevaux in Turbo Pascal, and recommended that we consider a similar approach. Although this would considerably
increase the scope of the effort, the potential 'technology transfer' value was very high, and we decided to proceed.
A team consisting of Nancy Fisher of the Computer Sciences Corporation (CSC), Journel, Froidevaux, Flatman, and the
authors, defined the philosophy and sketched the initial design for the system, drawing heavily on Froidevaux's example
for the 'look and feel* of the menu-driven user interface and integrated graphics. It was decided, among other things,
to program in FORTRAN, to try to stay entirely in the public domain, to use a simple ASCII data file structure, and to
target a hypothetical user with an AT and EGA graphics.
Suleiman Lalani of CSC provided a major boost to the software development by contributing the screen management
software used throughout the package. Chris Nisi of CSC coded the Dataprep and Trans programs. Melissa Robinson,
of CSC converted public domain graphics routines from the National Center for Atmospheric Research (NCAR) and used
them to develop the Xygraph, and Postplot programs. Naser Heravi and Russell Peterson of CSC provide on-going
maintenance and upgrades. David Gonzales of EMSL-LV wrote routines for identifying PC hardware configurations,
and assisted with the metacode device drivers.
We gratefully acknowledge the advice and encouragement provided by Andre Journel throughout the development
process. We are also indebted to the many people who provided constructive reviews of the software and user's guide,
including: Randal Barnes of the University of Minnesota, Dave Grundy of the U.S. Geological Survey, Stan Miller of
the University of Idaho, Brent Huntsman of Terran Corporation, John Rogers of Westat, and William P. Smith and James
C. Baker of the USEPA. Finally, we would like to thank the many users of version 1.1 who sent in the bug reports,
comments, and suggestions which made version 1.2.1 possible.
Evan J. Englund
Allen R. Sparks
Geo-EAS 1.2.1 viii Acknowledgements
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SECTION 1 INTRODUCTION
1.1 OVERVIEW
Geo-EAS (Geostatistical Environmental Assessment Software) is a collection of interactive software tools for
performing two-dimensional geostatistical analyses of spatially distributed data. Programs are provided for data file
management, data transformations, univariate statistics, variogram analysis, cross validation, kriging, contour mapping,
post plots, and line/scatter graphs. Features such as hierarchical menus, informative messages, full-screen data entry,
parameter files, and graphical displays are used to provide a high degree of interactivity, and an intimate view of results.
Users may easily alter parameters and re-calculate results or reproduce graphs, providing a "what if' analysis capability.
Geostatistical methods are useful for site assessment and monitoring situations where data are collected on a spatial
network of sampling locations, and are particularly suited to cases where contour maps of pollutant concentration (or
other variables) are desired. Examples of environmental applications include lead and cadmium concentrations in soils
surrounding smelter sites, outdoor atmospheric NO2 concentrations in metropolitan areas, and regional sulfate deposition
in rainfall. Kriging is a weighted moving average method used to interpolate values from a sample data set onto a grid
of points for contouring. The kriging weights are computed from a variogram, which measures the degree of correlation
among sample values in the area as a function of the distance and direction between samples.
Kriging has a number of advantages over most other interpolation methods:
Smoothing Kriging smoothes, or regresses, estimates based on the proportion of total sample variance
accounted for by random "noise". The noisier the data set, the less individual samples
represent their immediate vicinity, and the more they are smoothed.
Declustering The kriging weight assigned to a sample is lowered to the degree that its information is
duplicated by nearby, highly correlated samples. This helps mitigate the impact of
oversampling "hot spots".
Anisotropy When samples are more highly correlated in a particular direction, kriging weights will be
greater for samples in that direction.
Precision Given a variogram representative of the area to be estimated, kriging will compute the most
precise estimates possible from the available data. In practice, this is only approximated, as
the variogram must itself be estimated from the available data.
Estimation of the variogram from sample data is a critical part of a geostatistical study. The procedure involves
interpretation and judgment, and often requires a large number of "trial and error" computer runs. The lack of
inexpensive, easy-to-use software has prevented many people from acquiring the experience necessary to use
geostatistical methods effectively. This software is designed to make it easy for the novice to begin using geostatistical
methods and to learn by doing, as well as to provide sufficient power and flexibility for the experienced user to solve real-
world problems.
1.2 EQUIPMENT REQUIREMENTS
This system was designed to run under DOS (Disk Operating System) on an IBM PC, XT, AT, PS2, or compatible
computer. Graphics capability is not required, but is highly recommended, as most programs will produce graphics
output. Graphics support is provided for the Hercules graphics card, the Color Graphics Adapter (CGA), and the
Enhanced Graphics Adapter (EGA). At least 512 kilobytes (Kb) of random access memory (RAM) is required, but 640
Kb is recommended. An arithmetic co-processor chip is strongly recommended due to the computationally intensive
nature of the programs, but is not required for use. Programs may be run from floppy diskette, however, a fixed disk is
required to use the programs from the system menu. The system storage requirement is approximately three megabytes.
For hardcopy of results, a graphics printer (IBM graphics compatible) is required. Support is provided for plotters which
accept HPGL plotting commands.
1.3 Geo-EAS AVAILABILITY
Geo-EAS softwareand documentation are entirely in the public domain, and may be copied and distributed freely.
Geo-EAS 1.2.1 1-1 Introduction
-------
Executable code
Government agencies and academic or research institutions can obtain a copy of Geo-EAS executable code with user's
Guide at no charge by sending three preformatted high-density diskettes (5 1/4" or 3 1/2") to:
Evan J. Englund (Geo-EAS)
USEPAEMSL-LV.EAD
P.O. Box 93478
Las Vegas, NV 89193-3478
FAX: (702)798-2248
Others can obtain a copy for a distribution charge of approximately $45 (includes diskettes, User's Guide, and USA
shipping) from either:
ACOGS COGS
P.O. Box 44247 P.O. Box 1317
Tucson, AZ 85733-4247 or Denver, CO 80201-1317
FAX: (602)327-7752 Phone: (303)751-8553
Source Code
Geo-EAS source code is currently available only through ACOGS. A distribution charge of $91.50 includes source code
on 5 1/4" diskettes, a 600 page Programmer's Guide, and USA shipping.
1.4 USER PROFILE
To use this system, you should have some familiarity with personal computers, and DOS (Disk Operating System). You
should understand basic DOS commands such as DIR (Directory), CD (Change Directory), and how to insert and use
diskettes. For more information on these topics, consult a DOS user's manual. It is assumed that you have a working
knowledge of Geostatistics, and that you understand the basic Geostatistical concepts. For a list of references on the
subject of geostatistics, refer to Appendix A, References.
Geo-EAS 1.2.1 1-2 March 1991
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SECTION 2 SYSTEM SUMMARY
2.1 INSTALLING THE SYSTEM
2.1.1 The Distribution Diskettes
The distribution diskettes contain the files needed for system operation. Some programs require the presence
of a character font file in order to execute properly. Below is a list of the files which are included on the
distribution diskettes:
Program files:
GEOEAS.EXE
DATAPREP.EXE -
TRANS .EXE
STAT1.EXE
SCATTER.EXE
PREVAR.EXE
VARIO.EXE
XVALID.EXE
KRIGE.EXE
CONREC.EXE
POSTPLOT.EXE
XYGRAPH.EXE
VIEW.EXE
HPPLOT.EXE
Miscellaneous files:
HERSHY.BAR
EXAMPLE.DAT
EXAMPLE.GRD
METACODE.MET -
HPGL.PLT
HPSETUP.BAT
READ.ME
HPPS.COM
HPPS.DOC
HPPS.ASM
HPPSREAD.ME
2.1.2 Hard Disk Installation
the system menu program
data management utilities
data transformations
basic univariate descriptive statistics
scatter plots, linear regression
pair comparison computations for VARIO
variogram analysis and modeling
cross validation of parameters for KRIGE
2 dimensional kriging
contouring of gridded data
graphs of sample locations and values
2 dimensional line/scatter graphs
plots graph files on the screen
creates plotter files from graphic metafiles
character font file (required by CONREC,
POSTPLOT, XYGRAPH, VIEW, and HPPLOT.)
example data file
example gridded data file (for CONREC)
example graph file
example plotter instruction file
commands to set up plotter communications
additional "last-minute" information
screen-dump capability for HP LaserJet
document file for HPPS.COM
source file for HPPS.COM
information about HPPS.COM
To install the system on a fixed disk, a subdirectory should first be created (for example, GEOEAS). For
information about creating subdirectories, refer to the DOS reference manual. All files on the distribution
diskettes should be copied into the subdirectory. For more information on how to copy files from a diskette into
a subdirectory, refer to your DOS user's manual. Approximately three megabytes (3 million bytes) of storage
is required. If insufficient disk space is available for all files to reside together on fixed disk, programs must
be initiated from DOS and the system menu (GEOEAS.EXE) may not be used.
2.1.3 Using the Programs on Floppy Diskette
The fact that all programs and support files cannot reside on one floppy diskette has several implications. Since
the system menu program requires that all files be present on the same disk and subdirectory, the system menu
may not be used to run the programs; they must be initiated from DOS. Since several programs require the
presence of HERSHY.BAR to operate correctly, it is important that both the executable file and HERSHY.BAR
reside on the same diskette. Unfortunately, the size of the executable files for programs XYGRAPH,
POSTPLOT, and CONREC are too large to fit on the same 360 kilobyte diskette with HERSHY.B AR. This
means that if you only have 360 kilobyte disk drives (and no fixed disk) you will not be able to use these
programs. A separate working diskette may be prepared for each program, subject to the restrictions mentioned
above.
Geo-EAS 1.2.1
2-1
System Summary
-------
2.2 INITIATING THE SYSTEM
2.2.1 Using the Geo-EAS System Menu
A program has been provided on the distribution diskettes which allows access to all programs from a common
menu, called the System Menu. This file is named GEOEAS .EXE. Use of the system menu program requires
that all program and support files reside on the same disk and subdirectory (e.g. C:\GEOEAS). To start the
system menu program, type: GEOEAS .
A screen will be presented with the program names as in Figure 2-1. A highlighted box (cursor bar) will appear
on the screen. The cursor bar may be moved around the screen by using the , , , or
keys. When the cursor bar is positioned over a program name, a short description of the program will appear
at the bottom of the screen. To initiate the described program, press .
*** Note ***
The Geo-EAS system must have use of all available memory. No memory-resident programs such as SideKick
may be loaded, or the system menu program will not be able to load some programs. If an error message occurs
when using the system menu, try to initiate the desired program from DOS. If the program will not load
correctly, you must disable the loading of such memory- residentprograms, and re-start the computer. Programs
in which this is likely to happen are: Vario, Stall, Xygraph, and Postplot.
FfgnwjH
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Use arrow keys to Hove cursor, to select progran
s , '"/;
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Data preparation utilities
2.2.2 Using the Programs From DOS
To run the programs from DOS, type the program name at the DOS prompt For example, to start program S tat 1
type: STAT1
Geo-EAS 1.2.1
2-2
March 1991
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23 ANSWERS TO COMMON QUESTIONS ABOUT GEO-EAS
Q. How do you pronounce Geo-EAS?
A. Gee-oh-ease.
Q. Then how come it's not spelled Geo-EASE?
A. Next question.
Q. I can't run all of the Geo-EAS programs from the main menu. What should I do?
A. DOS 4.0 and higher version do not leave enough room in memory for some of the larger Geo-EAS programs
to run along with the menu. The only solution is to run them directly from DOS. This problem may also occur
with any version of DOS when memory-resident programs are present If executing from DOS doesn't work,
you may have to remove the memory-resident programs.
Q. How can I print Geo-EAS graphics on my Laser Printer?
A. We are now including a public domain utility on the Geo-EAS distribution diskettes which provides screen-
dump capability for HP LaserJet - compatible printers. Type the command HPPS before executing any Geo-
EAS programs, and you can then use the key to obtain hardcopy of any Geo-EAS graphic. (If
you use HPPS, do not use the
key). Alternate options for obtaining hardcopy include screen capture utilities
which are now part of many word processing packages such as WordPerfect 5.1, or stand-alone screen capture
programs such as InSet. These provide device drivers for a variety of printers.
Q. Is there a way to plot variograms, histograms and probability plots on my pen plotter?
A. No. Geo-EAS only provides plotter support for "metacode" files produced by three programs: POSTPLOT,
XYGRAPH, and CONREC.
Q. How do I create my own Geo-EAS file?
A. Geo-EAS does not provide any data entry or editing capability. Use your favorite text editor or word processor.
Retrieve an existing data file and edit it to match the Geo-EAS format, or type in the file from scratch. Geo-
EAS files contain several lines of header information, followed by a data table. The basic rules are:
The first line is a tide.
The second line contains the number (up to 48) of variables (columns).
The next n b'nes (one per variable) each contain the variable name and (optionally) unit and
format information.
The data table must contain one row per observation (usually up to 1000)
The data table must contain only numbers, in integer, decimal, or exponential (e.g. 5.6E6)
format, separated by blanks or commas. Variable columns need not be aligned.
Missing values must be indicated by the code " 1E31".
Q. Geo-EAS won't read my data file. What should I do?
A. Check to make sure that the number in line 2 is equal to the number of variable name lines and the number of
variables per row. Make sure that the data table contains no characters other than the exponential "E". If you
used a word processor or editor, make sure that the file was saved as an ASCII (or "DOS Text") file. If the file
was created or modified by Geo-EAS programs, it is possible that values were generated which are too large
for the format specifications, resulting in strings of "*" instead of the corresponding values. To prevent this,
expand the format specifications; or you can remove them entirely - the default isn't pretty, but should always
work. A final quirk-krige will not read a file from a floppy disk when the drive is specified in the Prefix field
with a backslash (e.g., a:\).
Q. KRIGE failed when I ran it using a Gaussian variogram model. What happened?
A. Unfortunately, the Gaussian model doesn't always work, particularily when you have a low nugget and/or
closely spaced data. The only solution is to use one of the other models.
Q. I have extra memory on my computer. Can I expand the data limits in Geo-EAS?
A. No. Not yet, anyway. Future releases of Geo-EAS will probably support more memory on DOS systems.
Geo-EAS 1.2.1 2-3 System Summary
-------
Q. Willtherebe: a) future upgrades? b) a 3-D version? c) additional utility programs? d)cp-kriging? e)probability
kriging? f) VGA and Super-VGA graphics? g) a VAX version? h) a UNIX version? i) a Macintosh version?
A. a) yes - see previous question, b) no - but see next question, c) yes. d) maybe, e) maybe. 0 probably, g) yes.
h) yes. i) probably not - but see next question.
Q. Is any other Geo-E AS-related software available that I should know about?
A. Yes:
SCOUT, a Geo-EAS file-compatible program, provides a number of capabilities useful for screening and
interpreting multivariate data: Two multivariate outlier tests; 3-D color scatterplots with real-time rotation; 2-
D scatterplots keyed to a color-coded correlation matrix; Analysis of "assignable cause" for outliers, with
expected-value ranges for the suspect measurements; Principal components analysis (PCA); Univariate
statistics and tests of normality. Scout can be obtained by sending a stamped, self-addressed mailer with one
pre-formatted high density disk (either 5 1/4" or 3 1/2") to:
Scout
Lockheed Engineering and Sciences Co.
1050 E. Flamingo Rd., Suite 251
Las Vegas, NV 89119
GEOPACK, a gepstatistical package developed at the EPA's laboratory in Ada, Oklahoma, includes capabilities
for disjunctive kriging and semi-automatic varipgram modeling. It can translate files between Geo-EAS and
GEOPACK applications. For current information on availability, contact
David M. Walters
U.S.EPA
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
GEOSTAT TOOLBOX, a geostatistical package developed by FSS International, shares a common ancestry
with Geo-EAS. The two packages have similar user interfaces, and still retain a degree of file compatibility.
TOOLBOX has 3-D capability. For current information on availability, contact:
The Support Group
19 winter St.
Reno,NV 89503
MGAP, a Macintosh program based on Geo-EAS has been developed by RockWare, Inc. and is in Beta Test.
It reportedly provides the capabilities of STAT1, VARIO, and KRIGE. The user interface, graphics, and file
structures have been modified for the Macintosh, but numerical results are reported to be identical to those from
Geo-EAS. For current information on availability, contact:
RockWare, Inc.
4251 Kipling St. Suite 595
Wheat Ridge, CO 80033
(303) 423-5645
Q. How will I know when new Geo-EAS versions/programs become available?
A. Fill out the form inside the back cover and return it to get on our mailing list.
Geo-EAS 1.2.1 2-4 March 1991
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SECTION 3 SYSTEM OPERATION
3.1 DATA
3.1.1 Geo-EAS Data Files
All programs in the system use a common format for data files. (Note: the term "Data File" is used to denote
a specific type of file used by Geo-EAS programs, as opposed to Pair Comparison files, Parameter files, or
Metacode files). Data files are simple ASCII text files which may becreated with any text editor. It is important
to be familiar with this format, and to make sure your data files are compatible, or the programs will not be able
to read them. An example data file has been included with the distribution diskettes. It is called "Example.dat".
Below is an explanation of the data file format.
Line 1 - Title
This line is a descriptive title which may contain up to 80 characters. Most programs display the title on the
screen when the file is read into memory. Some programs will use the title as the default title for graphics
screens.
Line 2 - Number of Variables (NVAR)
This line tells the programs how many variables are in the data file. The data are stored in rows and columns,
where each column contains a different variable, or measured quantity, and each row represents a different
sample location, time, etc. The data file may hold up to 48 variables (columns). Different programs have
different limits on the number of samples (rows) which can be read. Typically, up to 1000 samples may be read.
If a program encounters more than its limit of samples, the remaining samples will not be read into memory,
and will not be used for computation.
Line 3 to NVAR+2 - Variable Names and Measurement Units
The lines following the number of variables must contain the names and the measurement units for each variable
(1 line per variable). The variable name must be the first 10 characters in the line, and the units (optional) must
be characters 11 -20. When a data file is accessed by a program, the variable names are stored into toggle fields.
This allows one to select variables by name, and provides some internal documentation of data file contents.
Variable names will be used as default labels for graph axes, in graphic displays.
Optional Fortan "F" format statements may be added in columns 21 to 30 in the Variable name records in a Geo-
EAS data file. Programs such as TRANS and KRIGE, which create new Geo-EAS output files, can use these
to provide easier-to-read files. The format statement is in the form Fx.y, where x is the total number of columns
required by the variable, including decimal point and minus sign (if appropriate), and y is the number of digits
to be printed to the right of the decimal. TRANS will add a blank space between variables. For example, F6.2
will allow printing of any number in the range -99.99 to 999.99.
Line NVAR+3 To End of File - the Data Matrix
This is where the data are stored. Columns represent variables, and rows represent samples. The data may be
in "free format", which means that in a given line in the file, variable values must be separated by at least one
space, or a single comma. For readability, columns of numbers should line up, although this is not required.
Variable values must be numeric with no embedded blanks. In many cases, several variables may be present
in a data set, but for some reason a value could not be obtained for a particular variable in a particular sample.
A special value may be given to the variable in this sample which will indicate to a program that the value is
missing, so that it will not be used in calculations. The special value reserved for this is 1 .E31. This is "scientific
notation" for a 1 followed by 31 zeros. If your data set has missing values, be sure to type a 1.E31 where the
real value would have appeared. Below is a portion of the file Example.dat. It contains 5 variables and 60
samples.
Example.dat - Geostatistical Environmental Assessment Software
5
Easting feet
Northing feet
Arsenic ppm
Geo-EAS 1.2.1 3-1 System Operation
-------
Cadmium ppm
Lead ppm
288.0 311.0 .850 11.5 18.25
285.6 288.0 .630 8.50 30.25
273.6 269.0 1.02 7.00 20.00
280.8 249.0 1.02 10.7 19.25
273.6 231.0 1.01 11.2 151.5
276.0 206.0 1.47 11.6 37.50
285.6 182.0 .720 7.20 80.00
288.0 164.0 .300 5.70 46.00
292.8 137.0 .360 5.20 10.00
3.1.2 File Naming Conventions
Only valid DOS file names will be accepted by the programs. For more information on DOS file names, refer
to the DOS reference manual. All file names used by the Geo-EAS programs are associated with a File Prefix.
The File Prefix provides a means of specifying a drive, or subdirectory where data files should be accessed. This
option is discussed in detail in the section below (Common Menu Options). Although the programs place no
restriction on file extensions, it is good practice to use consistent naming conventions for file extensions. Below
are the suggested extensions which are used as defaults in Geo-EAS programs.
Geo-EAS File Extensions:
.TXT - an ASCII text file
.DAT - a Geo-EAS data file
.PCF - a pair comparison file, created by PREV AR, read by V ARIO
.GRD - a gridded Geo-EAS data file (could be produced by KRIGE)
.CPF - CONREC parameter file
.KPF - KRIGE parameter file
.XPF - XYGRAPH parameter file
.POL - Polygon boundary file, used by KRIGE
.MET - metacode (graph) file, created by CONREC, POSTPLOT, and XYGRAPH, and used by
HPPLOT, and VIEW
PLT - plotter instruction file, produced by HPPLOT
3.13 System Defaults Option
This option allows you to disable the introductory screens which appear when programs are initiated. The
System Defaults File (GEOEAS.DEF) contains defaults for the programs to use at start up. The first record
contains the most recently used File Prefix. The second contains the most recently used data (.DAT) file name.
These records are automatically updated when a program is terminated, so that this information may be passed
to the next program used. If the file does not exist when a program is started, it will be created when a program
is finished. A third record has been added to GEOEAS.DEF to allow you to disable the introductory screens.
This record contains the characters "INTRO=ON". To disable the introductory screens, use a text editor such
as IDLIN to change the "ON" to "OFF".
Geo-EAS 1.2.1 3-2 March 1991
-------
3.2 INTERACTIVE SCREENS
3.2.1 Screen Format
All Geo-EAS programs have similar interactive features. Each program uses interactive screens for selection
of program options and display of results. The screens are composed of several common components. Figure
3-1 displays an example interactive screen from program Stall. Below is a description of the common
components.
***
Ex8»j>le1afeiro$|'?is
Sejrtsea
(A.^ A progran to conpute unlvarlate descriptive statistics
File Prefix: c:s6eo!ftS\IlaU\
File
lata File Mane
Uariable
UarUble
Height
Log Option
Lin its
HinlMM
HaxlmiM
Exanple.dat
: Cadnlun ^_^
None fr^i
: Off \^/
.690
16.700
1 Variables : 5
t Data records : 60
• Hissing Data : 0 CZ Obs<=9>
Execute
Use this option to conpute
display the statistics. A
of additional graphs and o
vill be displayed.
and
Menu
ptiotis
(B.)
Prefix Data Uariable Units
Conpute basic descriptive stats
Batch Statistics Quit
A. The Screen Frame
This is the large double-line rectangle which encloses each screen. Program inputs and results are displayed in
this area. Typically, the screen frame is subdivided into smaller single- line rectangles. Each of these smaller
rectangles contains a functionally-related group of one or more input parameters, or program results.
B. The Message Line
This is the double line rectangle at the bottom of the screen frame. This area is used to display program error
messages, yes/no prompts, prompts for additional information, or instructions for using a program option.
C. The Menu Line
This is the line of text located just below the screen frame. It contains a set of menu option names and a
highlighted box (cursor bar). The cursor bar can be moved along the menu line by using the , and
cursor control keys. As the cursor bar is moved over a menu option name, a short description of the menu option
is displayed on the line just below the menu line. This line is called the menu description line. In addition, on
the main screen for each program, more detailed descriptions of the menu options are displayed. You may
explore the possible choices in a program by moving the cursor bar and reading the descriptive messages which
accompany each menu option. To select a menu option, move the cursor bar over the desired menu option name,
and press . An alternative (and faster) way to select menu options is to press the key which corresponds
to the first letter in the menu option name. The result is the same as using the cursor control keys, and pressing
. In program Stall for example, you would choose to enter the data file name by pressing (for the
Data option) from the main menu.
D. Parameter Groups
Typically, a functionally-related group of program input parameters (fields) are enclosed together on the screen
by a single-line rectangle. These groups of parameters are accessed through the menu. When a menu option
is selected (as described above), a cursor bar appears at the screen field, and a message describing what action
to take appears on the message line. When such a group contains several fields, the cursor control keys, or
are used to move to subsequent fields. Exiting from the last field in the group will return the cursor
bar to the menu line. In some programs, parameter groups are arranged in a tabular fashion (rows and columns).
To return to the menu line from such a group, move the cursor bar to the left or bottom of the group with the
or keys.
Geo-EAS 1.2.1
3-3
System Operation
-------
3.2.2 Types of Screen Input Fields
Several types of input fields are provided to allow flexibility in program parameter specification. Below is a
list of these types, and an example of each field type in the Stall screen:
Alphanumeric Fields
Numeric Fields
Toggle Fields
Yes/No prompts,
prompts for additional
information
These fields may contain character strings of alphabetic or numeric characters. Any
alphanumeric characters may be entered. The "Prefix", and "Data" menu options in Stall
require alphanumeric values to be entered. To specify a data file name, select the Data option
on the menu, and type the name of ihe inpul date file.
Only numeric date may be entered into numeric fields. Some numeric fields will only accept
integer (non- decimal) numbers. The programs will respond to any erroneous keystrokes
(such as alphabetic keys) with a low- pitched error tone. An example of numeric fields in
program Stall are ihe two fields accessed through the Limits option Only numeric values may
be entered into ihese fields. Values musl be entered in the conventional manner (legal
characters are <0> ihrough <9>, and <.>, exponential nolalion for numeric values is nol
allowed.)
A toggle field is a special lype of field which contains a lisl of 2 or more presel choices. Only
one of these choices is displayed in the field. The key is used to change the displayed
choice, and the key is used to make the selection. Two examples of toggle fields in
program Slatl are the "Variable" field and ihe "Log" field. Once a file name has been
specified, Ihe "Variable" toggle field will conlain Ihe names of all variables in ihe file. When
ihe Variable option on ihe menu line is selected, ihis field will be highlighted, and each time
Ihe key is pressed, a new variable name will appear in ihe field. When ihe desired
variable name appears, press Ihe key to selecl it The "Log" field is an example of
a toggle field with only two choices ("On", or "Off'). If "On" is chosen, then statistics will
be calculated for the log of the selected variable.
These prompts are for information which will not be displayed permanently on ihe screen.
They will appear temporarily on the message line. A Yes/No prompt will typically have the
form: "Question...?". To respond Yes, press the key, to respond in the negative,
press any other key. A typical Yes/No prompt is Ihe "Do you really want to Quit ?"
prompt which is displayed after ihe "Quil" (terminate program) option is selected. Some
menu choices will resull in prompts for additional information. These prompls for additional
information will appear on ihe message line and may be of Ihe alphanumeric, numeric, or
toggle lype.
Geo-EAS 1.2.1
3-4
March 1991
-------
(e.g. CONREC). Typically, this option will provide access to one or more toggle fields which contain the
variable names. Some programs include additional fields for selection of other parameters related to the choice
of variables. These will be explained in the particular section which describes the program.
Execute
This option is common to all Geo-EAS programs. It is used to initiate processing of data by the program.
Although the processing and interaction subsequent to the selection of this option is different for each program,
it shares the common function of initiation of processing. The individual differences in processing will be
described in more detail in the subsections which describe the programs.
Read Parameters, Save Parameters
These options are common to all Geo-EAS programs which make use of "Parameter Files". Parameter Files
are files which contain values for all parameter choices available in a particular program. If a program provides
this feature, you may save the values of parameters for later use, by using the Save Parameters option. Selection
of this option will result in a prompt for the output parameter file name. The File Prefix is used to create or access
the file. The Read Parameters option is used to load the parameter values into the program. When this option
is selected, an input parameter file name must be entered. Typically, a program will attempt to load all data and
set all parameter values based upon the information in the input parameter file. It is assumed that the data file
associated with the parameter file is in the same location (subdirectory, etc.) as it was when the parameter file
was saved. If any errors occur while accessing or reading the parameter file or the associated data file, an error
message will be issued and the program will re-initialize all parameter values to their defaults. Conventions
should be used when naming parameter files so that they can be associated with the appropriate data files and
programs. A suggested convention for file extensions is given in a previous section (File Naming Conventions).
It is also suggested that the first part of the file name have some similarity to the associated data file name.
Quit
This option is common to all Geo-EAS programs. It is used to exit from a menu, or program. Using the analogy
of the Menu Tree, the quit option allows you to "move up" one level in the tree. When the quit option is used
from the main menu of a particular program, a Yes/No prompt is issued: "Do you really want to quit
?". The key is typically used to select this option. The Yes/No prompt is a means of ensuring that a series
of keystrokes will not cause inadvertent termination of the program.
3.3 Geo-EAS GRAPHICS
3.3.1 On-Screen Graphics
Many Geo-EAS programs have graphics capability. Each such program uses graphics in one of two ways.
Programs Stall, Vario, Xvalid, and Krige plot graphics directly on the screen. This approach is used to provide
a quick look at data, or program results. Such graphics displays may be printed on a dot-matrix printer, but may
not otherwise be saved or modified. When a graphics screen is displayed, the program will wait for a key to
be pressed. Pressing will cause an interactive screen and menu to be displayed. Pressing
will produce
a hard copy of the screen on a dot matrix printer, (see Section 2.3 about laser printers). It is important to make
sure that a graphics printer is connected to your computer if you choose this option, or the program will "lock-
up". Also make sure that the printer is turned on and "online". If the program "locks up", you will probably
have to re-start the computer. (See the section on Error and Recovery Procedures for more information).
3.3.2 Metacode-Based Graphics
Postplot, Xygraph, and Conrec also plot graphics on the screen, but only after writing a "metacode" file. A
metacode file is a file of device-independent plotting instructions. These files can be used later to redisplay the
graph on the screen, or to plot it on a pen plotter. Internally in these programs, the metacode is written by a set
of public-domain FORTRAN subroutines produced at the National Center for Atmospheric Research (NCAR,
in Boulder, CO.) by their Scientific Computing Division. These files are used by special translator programs
called "metacode translators", which convert the metacode into device-specific graphics commands. Currently,
only two metacode translators are provided. Program View translates metacode into video graphics for EGA,
CGA, and Hercules graphics hardware, and program Hpplot will convert metacode into HPGL (Hewlett
Packard Graphics Language) plotting instructions. Each metacode-producing program uses a version of view
to display the graphs during an interactive session. Since producing and translating metacode takes longer than
sending graphics commands directly to the display, these programs take longer to draw graphs than die non-
metacode producing programs. The advantage to using metacode is the capability of obtaining higher-quality
graphic output on a pen plotter or other graphics device.
Geo-EAS 1.2.1 3-6 March 1991
-------
3.4 ERROR AND RECOVERY PROCEDURES
Known "bugs":
Xygraph or Postplot may fail when certain incompatible combinations of axis tickmark parameters are chosen. This is
dependent upon the data configuration and choice of parameters, and is due to internal limitations in the NCAR graphics
utilities which these program use.
Postplot may produce undesirable scaling in plots with certain sample data configurations. An attempt is made by the
software to produce "true-proportion" post plots. The underlying NCAR utilities which produce the metacode files
sometimes override the scaling specified by Postplot. This is an unexplainable phenomenon which has not and
unfortunately will not be corrected.
Trans may crash when an operation is chosen which would produce a very large or very small number. An example would
be the operation 1.0 / X, or 10 **X, when X is very small or very large (l.E-1000,1.E1000). This type of program error
cannot be trapped or handled by Trans. In such cases the result cannot be produced due to hardware limitations in the
precision of the numeric coprocessor (or floating-point emulation software). Since there is no remedy for this situation.
The only solution is to avoid such operations.
Avoiding User-Induced Errors:
There are several error conditions which the program was specifically not designed to check for. These involve checking
to see if disk or printer peripherals are connected and ready for data transfer. You are responsible for ensuring that printers
are attached and online, or that disk drives have the correct density media and are ready for read/write operations, when
Read Save, or Write options are selected. The following actions are guaranteed to create a "lock-up" situation.
Trying to print a text or graphics screen when the printer is not connected, or on-line. If a printer is connected, make sure
it is turned "on", and is ready to accept output from the computer (on-line). If no printer is connected to your system you
may have to "re-boot" the computer (in this case, you should avoid trying to print a text or graphics screen in the first
place).
Accessing a file on a floppy diskette drive when the disk drive door is open.or no diskette is present. In some cases, DOS
may respond with a message: Device not Ready (Abort, Retry, Ignore). Insert a diskette and press (for Retry). If
this does not work, you must re-start the computer.
Geo-EAS 1.2.1 3-7 System Operation
-------
SECTION 4 USING Geo-EAS IN A GEOSTATISTICAL
STUDY: AN EXAMPLE
4.1 OVERVIEW
This section will demonstrate how to use Geo-EAS software to conduct a geostatistical study. Starting with an example
data set from a hypothetical pollution plume, you will work through a complete study, using many of the Geo-EAS
programs in the process. Of necessity, this exercise will be somewhat abbreviated. We will conduct a relatively
straightforward study, illustrating the options which are likely to be most commonly used. The data set (example.dat)
has been included with the software, so that you may repeat the exercise as a tutorial, or to test the software.
The scenario for the example is that data has been acquired from analyses of 60 soil samples at a site contaminated with
arsenic, cadmium, and lead. The basic objectives are to examine the data set for possible errors or outliers, and to
construct contour maps of each of the variables to define the areas of highest concentration. In this example you will
work primarily with the variable Cadmium; you are encouraged to try out these procedures with the arsenic or lead data.
The Example Data Set
The Example.dat data set is an ASCII file in the Geo-EAS format. It contains data from 60 sample locations. The file
structure is described in Section 3 above. The first few lines are as follows:
Example.dat - Geostatistical Environmental Assessment Software
Easting feet
Northing feet
Arsenic ppm
Cadmium ppm
Lead ppm
288.0 311.0 .850 11.5 18.25
285.6 288.0 .630 8.50 30.25
273.6 269.0 1.02 7.00 20.00
280.8 249.0 1.02 10.7 19.25
4.2 EXPLORATORY DATA ANALYSIS
The first order of business in any data analysis is to become familiar with the data set. You will use a combination of
statistics and graphical displays to look at the range and shape of the frequency distribution, to look for data outliers which
may be erroneous or unrepresentative, to look at the "spatial coverage" of the data, and to look for spatial patterns in the
data.
Begin by taking a look at a map of the data produced by the program Postplot. Assuming that you have already copied
the software and data into a directory called Geoeas on your hard disk, and have used the command "CD \Geoeas" to
access the directory, you can run Postplot either by:
(1) using the DOS command C:\GEOE AS> Geoeas to enter the system menu, moving the cursor
to the Postplot option with the arrow keys, and pressing , or by
(2) running the program directly from DOS by typing the command C:\GEOEAS> Postplot .
When the program begins execution, it first displays a screen with introductory information. When you press a key to
proceed, you will see the program main screen and menu, as displayed in Figure 4-1.
The bottom line on the screen provides the list of available options. The first five move you to an area on the screen (or
to a new screen) where you can input or select program parameters. The Execute option starts the actual processing
portion of the program, and Quit moves you to Uie preceding menu (or out of the program). All menus in the system
operate in a similar way: options are selected by moving the highlighted bar to the desired option name with the arrow
keys and pressing , or by typing the first character of the option name.
Geo-EAS 1.2.1 4-1 March 1991
-------
fl prograH Tor plotting 20 sample locations and walucs
File Prefix : C AGeoEAS\DalaS
Data : Exanple.dat
Variables
X coordinate variable : Easting
V coordinate variable : Northing
Variable to post : Cadniun
Options
Include Values : Ho Size : 5
Scale Factor : 19" 6
1 Declmls : 1
Include Son bo Is: 1 Size : 4
Netacode File : HeUcode.net
Execute
Use this option to create the
plot. The plot will be saved in
the file specified.
w
Prefix Data Variables Options Graph Options
Generate the plot
Quit
*** NOTE *** Whenever feasible, the programs will use default options and values. These may be preset,
computed from the available data, or passed from a previously run program. Be careful! The computer doesn't
understand your problem or your data. Defaults make it easy to get a result quickly, not necessarily to get an
appropriate result In this example we will usually use the defaults to get quick results. Try other options to get
familiar with the full range of system capabilities.
In Postplot, the minimum that you MUST do to obtain a plot is:
1. Use the Data option to enter the name of a Geo-E AS data file (or accept the default name, if one is
provided).
2. Use the Variable option to select the X and Y variables and the desired variable for posting (or accept
defaults).
3. Use the Execute option to enter a name for the metacode file (or accept the default), create the metacode
file, and display the map.
In this case you can skip the Prefix option because the data file is in the Geoeas directory, and enter the file name
Example.dat with the Data option. The program reads the data file, and automatically executes the Variable option. The
program assumes that the X and Y variables are the first and second in the file, respectively. This is correct, so you should
accept both by pressing twice. The program also assumes that the third variable is the one we want to post This
is incorrect - we want Cadmium, not Arsenic - so use the key to toggle through the list of variables until Cadmium
is found, and then press . Now use the Execute option; it will move you to the metacode file name field. Accept
the default metacode file name (Metacode.met is effectively a permanent scratch file) and wait for the plot to appear on
the screen. After examining the plot, hit to return to the main menu, and use the Quit option to return to the system
menu (or DOS).
To simplify our explanations in the future, an abbreviated notation for the above sequence of events will be used. A
general formula exists for each option: initiate the option; then take one or more actions, each of which may result in a
screen field taking a particular value. The above sequence thus becomes:
OPTION
ACTION
FIELD
VALUE
DATA
VARIABLE
EXECUTE
QUIT
Enter
Accept
Accept
Select
Accept
Answer
Data File
X
y
variable
metacode file
Example.dat
Easting
Northing
Cadmium
Metacode.met
Y
The resulting Post plot is shown in Figure 4-2.
Geo-EAS 1.2.1
4-2
Tutorial
-------
?'?' f
•f'ff $f
Poatplot of Cadmfum from data fil« •xampl«.dat
300
1«l Quariil*
2nd Ouartfl*
3rd Quartiln
•4th Quartll*
Eaatfng (feat)
.000 m + m o,3oo
0.300 < x « 7,000
7.000 < n * 10.000
1O.OOO < * • 1 ft.TOO
J""'
From this plot you can see that the samples fall in a rectangular area about 250 by 220 feet. The sample locations are
irregularly spaced, and although there are some gaps and clusters, they provide relatively uniform coverage over the
entire rectangle. The symbols/colors represent the quartiles for the cadmium values, with */red as the upper quartile, and
+/blue as the lower. A general trend can be seen in the cadmium values: The highest values occur in a rough E-W band
through the center of the plot, while the lowest fall in parallel bands at the north and south margins. The * in the northwest
corner of the area seems to be an exception to the trend; it seems too high compared to its surroundings. Such "spatial
outliers" should be checked to confirm that their coordinates and data values are valid. For this example, you will assume
that this sample is valid.
While the plot is on your screen, you will note that there is no menu line at the bottom. What do you do now? Every
graphics screen actually has two "invisible" options available -
(Print) and (Quit), which produces a screen dump
on your printer, and returns you to the main menu, respectively.
*** NOTE *** Don't try a screen dump if your printer is not connected and turned on - the program will "hang
up" and you will have to re-boot with --!
Now you should use program Stall to generate some statistics on the data. When Stall is initiated, the Main screen will
be displayed as in Figure 4-3.
vX %
f ffff -&s fj.-fj.j- •&
':', 'r-X'WM A
V
"'" t,*
''"$?!{' f'', %
•?\', » " •¥<•" ' "!'''
',',, , , ' 'V ''•>'
,,;',' ', # •.
<• m *J'/s , i
•l* " ,' 5
A program to conpute uniuariate descriptlue statistics
File Prefix: C.AGeoBftS\BataV
File
Data File Nane : Exanple.dat
Variable
Variable : Cadnlun
Height : Hone
Log Option : Dtt
Limits
HlnlnuH : .008
HaxlMin : 16.760
« Variables : 5
1 Data records : 60
I Hissing Data : 6 (2 Obs<=0)
Execute
Use this option to compute
display the statistics. A
of additional graphs and o]
ulll be displayed.
and
menu
jtlons
Prefix Data Variable Limits [
Compute basic descriptive stats.
Batch Statistics Quit
Geo-EAS 1.2 J
4-3
March 1991
-------
The option sequence below is the minimum required to compute univariate statistics and display a histogram and a
probability plot for the variable Cadmium. Note that a default file name (Example.dat) has been carried forward from
the previous program. When you finish examining the histogram, you do not go directly back to the main menu; an
intermediate menu lets you select alternate options for replotting the histogram.
COMMAND
ACTION
EXECUTE
HISTOGRAM
QUIT
PBABILITY PLOT
FIELD
VALUE
DATA
VARIABLE
Accept
Select
Accept
Accept
Data File
variable
weight
log option
Example.dat
Cadmium
None
Off
The univariate statistics, histogram, and Probability plot are generated. Figure 4-4 displays the univariate statistics for
cadmium. Figures 4-5 and 4-6 display the histogram and probability plot for cadmium.
Sfail Results Screen
Data File : C:\GeoEAS\Data\Exanple
Variable : Cadniun
Lower Unit :
Upper Unit : 16
I Obseruations 60
1 Hissing Data 0
1 Retained 60
(lean
Uariance
Std. Deviation
xCoeC. Uarintlnn
Skew ness
Kurtosis
.060
.769
7.8850
15.5315
3.9410
4.9.9009
-.1510
2. -1639
riJMeEl
dat
Sun of Heights :
HininuN Ualue :
25th Percent ile •
nedian :
75th Percent lie :
naxlwin Ualue
66.6006
.6006
5.3006
7.9506
16 .0006
16.7000
Probability Plot Exanine Quit
Choose histogran parameters / display graph
Cadmium
Histogran
Data file: exaNple.dat
1 1 i! 1 1
9.
\ *•'
It
3.
a.
a
—
"^
—
—
—
—
-
1
4. 8. 12.
Cadniun
-------
Horful Probability Plot for Cuhlua
D*t. fll.; •xwli.il>>
»e.
14.
5 "•
<
' «.
4.
1. ""
4«(
>
>
/
<"
/
/*
i"
f
•t>tlitlo«
N Tot4l It
» Hi» •
N Und M
NHn 7.189
Vvltno* 15.531
ltd. On I. Ml
ScMf.Vir 4».W1
ttOTK« -.151
KutocU 1.4*4
Hlnliui .Ml
tSth X 3. Ml
Mini 7.Wi
TMh X K.IM
Nulmm U.7M
18 38 90 71 99 f?
CuMulitlv* Pvrewit
, ,
\fftS JV f fJfff
From the histogram and the statistics, it can be seen that this data set is nearly symmetrical about the mean value (the
mean is close to the median, and approximately halfway between the minimum and maximum values). There are no
suspect outliers. The probability plot shows that the data set approximates a normal distribution (a probability plot is
a cumulative frequency plot scaled so that a normal distribution plots as a straight line). Whether a distribution is normal,
log-normal, or something else has no particular geostatistical significance, except that it is often more difficult to interpret
variograms for highly skewed distributions such as the log-normal, and in such cases it may be useful to also compute
variograms on log-transformed data.
VARIOGRAM ANALYSIS
The computation, interpretation, and modeling of variograms is the "heart" of a geostatistical study. The variogram
model is your interpretation of the spatial correlation structure of the sample data set. It controls the way that kriging
weights are assigned to samples during interpolation, and consequently controls the quality of the results.
All interpolation and contouring methods make the assumption that some type of spatial correlation is present, that is,
they assume that a measurement at any point represents nearby locations better than locations farther away. Variogram
analysis attempts to quantify this relationship: How well can a measurement be expected to represent another location
a specific distance (and direction) away? Experimental variograms plot the average difference (actually, one-half the
squared difference, or variance) of pairs of measurements against the distances separating the pairs. If you had
measurements at all possible sample locations, you could compute the "true variogram" for a site, i.e., the variance of
all pairs of measurements which satisfy each combination of distance and direction. In practice, with limited data, you
compute the variances for groups of pairs of measurements in class intervals of similar distance and direction. You then
plot a graph of the variances versus distance for a particular direction, and fit a model curve to the graph; the model is
assumed to be an approximation of the "true variogram".
Continuing with the example, we will use Prevar to create an intermediate file of data pairs, and Vario to compute, plot,
and model variograms. No automatic model fitting is provided; we will use Vario to superimpose plots of various model
curves on the experimental variogram until we find one that looks right.
Prevar is a simple program with only a few options to allow you to reduce the number of sample pairs in the output file
to the maximum allowed by Vario by setting minimum and maximum limits on X and Y, and by setting a maximum
distance for pairs. This is necessary when the number of samples in the data set exceeds 181. Upon initiating Prevar,
the main screen will be displayed, as in Figure 4-7.
Geo-EAS 1.2.1
4-5
March 1991
-------
Preyar Main Screen
rile Freflx
••J:B*ll?l:«WtlMlll
A preprocessor for program VARIO
: C:sGeoEAS\DataS
riles
Data rile: Exanple.dat
Fair Comparison rile: Example. pcf
Variables
>
Limits
X:
V:
Distance:
Variable: Easting
Variable: Northing
ninlnun Maximum
Z51.109 132.060
118.309 315.000
.000 308.647
Variables : 5
Records : 66
Fairs possible: 1779
Fraction: 1.000 Seed
Max: 16384
: 1951
Execute
Select this option to build the
pair comparison file. Distances
and directions for all pairs "ill
be computed • sorted and saved.
Prefix Files Uariables Limits Subset
Build the pair comparison file
Quit
The random seed may be different in what you actually observe on your screen. Select the subset option and change the
seed to 1951. The option sequence below creates the pair comparison file Example.pcf.
OPTION
ACTION
FIELD
VALUE
Accept
Accept
Data File
Pairs File
FILES
EXECUTE
Next, initiate Vario, and the Vario Main screen is displayed, as in Figure 4-8.
Example.dat
Example.pcf
Ffgura 4-8
• HM:Mi.W«Mli» i
fl program for conputlng <»rlograms
File Pref ix:C:NCeoEflSM)ata\
File
Pair Conparison File: Cxanple pcf
Variable
Variable: Cadniun
Log Option: Off
Limits
Hinlnun 000
Maxinun: 16.700
Uars : 5 » Kept
Data : 60 1 Obs<=0
Pairs: 1770 * Missing
60
Z
: 0
Variogran Options
Use this option to display the
Uarlogran Options Screen and menu.
Variogran options may be selected
and the uarlogram may be computed.
Prefix Data Variable Linits jM
Specify uariogran options, conpute
Quit
The following option sequence reads the pair comparison file into memory, and moves to the next menu:
OPTION ACTION FIELD VALUE
DATA
VARIABLE
Accept
Toggle
Accept
Pairs File
Variable
Log Option
Example.pcf
Cadmium
Off
OPTIONS/EXECUTE
Geo-EAS 1.2.1
4-6
Tutorial
-------
The Options/Execute menu allows us to specify how we want the experimental variogram to be computed. This screen
and menu is displayed in Figure 4-9.
I wmmt
Uar table :Cadnlun
niniMM : .000
naxlMiui : 16.7
Lag
1
Direction : .600 2
Tolerance : 30.600 3
Ibx Banduidth: MAX 4
S
7
Lag Spacing 0
9
NlnlMlM .000 10
HaxiMW 302.362 11
Increment 15.134 12
MiKtm
fair Tile
Nin. Distance
tax. Distance
Distance Lag
15.194 13
30. SUB 14
45.582 15
60.776 16
75.970 17
106.358 19
121. 5S3 20
136.747 21
151.941 22
167.135 Z3
182.329 24
Eumple.pcf
6.06
302.
Distance
197.523
Z12.717
227.911
243.1»5
258.299
288.687
303.681
'AUIJIB Hew Lags Change Lags Post Plot Execute
cify pair orientation (selection) criteria
Quit
ii
' ''.' , ,'"'<'
First, specify the distance class intervals (lags) and directional tolerances for computing the variogram. Finding the
"right" combination is a trial and error exercise, but a systematic approach can be helpful:
To start, you will use the default direction, which is an "omnidirectional" variogram. The angular tolerance of 90 degrees
on either side of any specified direction line allows all pairs to be included regardless of direction. This maximizes the
number of pairs in each distance class, which usually gives the "best" or smoothest variogram. See Figure 10-3 in Section
lOfor an more detailed illustration of the direction parameters. From this omnidirectional variogram we can usually get
the best estimate of the y-intercept (nugget) and maximum value (sill) parameters for the variogram model, as well as
the best idea of what type of model(s) should be fitted.
Next, try several different lag intervals for plotting the experimental variograms. You are trying to obtain the maximum
detail at small distances, (i.e., small lags) without being misled by structural artifacts due to the particular class interval
used. You will have more confidence in a model if it fits experimental variograms computed at several different lag
intervals.
The default lag intervals are computed from a rule-of-thumb which states that variograms are generally not valid beyond
one-half the maximum distance between samples. Round these to the more convenient numbers of 150 and 15, and plot
the resulting variogram (Figure 4-10), as follows:
OPTION
ACTION
FIELD
VALUE
NEW LAGS
EXECUTE
PLOT
Accept
Input
Input
Minimum
Maximum
Increment
0
150
15
Geo-EAS 1.2.1
4-7
March 1991
-------
28.
14.
k 12.
I
> 8.
4.
1.
a
VariO9rafi for CadHiun
I • " ' 1
X
I
1
49. 88. 128. 14
Distance
File iexawle.poF
Pain : 1388
Direct • .888
Tol. : 98.888
HaxBand: n/a
Cadniun Llniti
Hininun' .888
Haxinun: K.7BB
Mean : 7.885
Var : 1SJ73
9.
^
S"
f f
'' ,
'i ^
" arrow key can be used to exit the model option). The
resulting graph is displayed in Figure 4-11.
OPTION
ACTION
FIELD
VALUE
MODEL
MODEL
Input
Toggle
Input
Input
Nugget
Type
Sill
Range
5
Spherical
11
80
PLOT
Varlogrui fgp C*dniun
FiU
Pain
Direct.
Tol.
ItaxBand
Cadniun
Minii
Itanium
Hean
Var.
7.885
15.273
Geo-EAS 7.2.7
4-8
Tutorial
-------
This model fits reasonably well at the nugget and sill, but the initial slope is too steep, indicating that the range is too low.
It appears that the curve would fit well if it were shifted about 25% to the right, so you should try again with a range of
100:
OPTION
MODEL
ACTION
Accept
Accept
Accept
Input
FIELD
Nugget
Type
Sill
Range
VALUE
5
Spherical
11
100
PLOT
The resulting graph is displayed in Figure 4-12.
Viriowan for Cftdniun
File :exanple.pGf
P»ir« : 1188
Dirat.
Tol.
ra.ua
n/t
Cvtilun Llniti
lUnlnun:
HMimn:
n«n :
V«r
7.883
is.m
This is an excellent fit; about as good as you can get with a spherical model. That low fifth point, however, suggests that
an exponential model which has a more gentle curvature may also provide a good fit. (If you are unfamiliar with the four
types of models available in VARIO, repeat the option sequence above three more times, changing the model type each
time.) Abitof trial and error leads loan exponential model with a nugget of 4.5, sill of 13.5, and range of 160. This graph
is displayed in Figure 4-13.
OPTION
MODEL
ACTION
Input
Toggle
Input
Input
FIELD
Nugget
Type
Sill
Range
VALUE
4.5
Exponential
13.5
160
PLOT
Some obvious questions that come up at this point are: Which one of these models is best? How do you decide which
one to use? What happens if you pick the wrong one? Unfortunately there aren't any simple answers. The best model
is the one which most closely matches the true variogram for the site, but of course, you will never know what that is
unless you exhaustively sample the site. Although some form of least squares criteria could be used, in Geo-EAS the
selection must be made subjectively, simply by picking the model that looks like the best fit. Sometimes the error
distributions obtained from cross-validation can help you to decide which. Fortunately, the differences between the
spherical and exponential models above will only cause minor differences in the kriged estimates, so that either one would
be an acceptable choice.
If you look at variograms computed at different lags, it will become obvious that the experimental variograms contain
quite a bit of noise. The shape of the experimental variogram changes as the lag spacing changes, and the model which
appears to fit best at one lag spacing may appear to be the worst at another. Try a lag spacing of ten units. The graph
of Figure 4-14 will be displayed.
Geo-EAS 1.2.1
4-9
March 1991
-------
Varlo9~*n for Cacbiiun
f f f t f f f tf ff f S
-------
Now repeat the above option sequence with a lag increment of 25. The resulting graph is displayed in Figure 4-15.
Model *
Vtriogran for
Film :«xanpl*.f»of
P«in : 1*42
Dlr«ot.: .MO
Tol. : 90.000
M.xB.rx): n/«
C»dniuii Llniti
Mlnlmm. .860
Haxinim: 1« 700
H»n : 7.839
Vir 15^73
*v
-' /'i''k#W«^
''IV 'A;
',,"'' ' '.'
¥-'?>„ ""# *'""
' "",/ ,,.;
•4, ,'?, t'Sf'l
>"*,'. . ;?v
As you can see, the ability to define the "true" variogram structure is limited by the particular set of data available. The
best you can do is to find a model which fits reasonably well over a range of lag spacings. Both of the two models proposed
earlier are satisfactory. In practice, kriging estimates calculated with the two variogram models will be almost identical.
Kriging standard deviations however, are more sensitive than the estimates to changes in the variogram model, as well
as to differences between the "real world" and the assumptions underlying the kriging equations. For this reason, it is
generally not wise to interpret kriging standard deviations as a true measure of the estimation error. For the remaining
discussion of variograms the exponential model will be used.
At this point in the structural analysis, anisotropy is the major remaining question. When you looked at the post plot of
the data, there appeared to be a tendency for similar values to form elongated E-W bands. Now you want to see if
directional variograms confirm this effect. Like lag spacings, directions and angular tolerances require a trade-off
between resolution and precision. If you plot four directional variograms at angles of 0,45,90, and 135 degrees, with
a tolerance of 22.5 degrees, you have effectively divided the pairs in our omnidirectional variogram into four subsets.
This causes an increase in noise comparable to reducing the lag spacing by a factor of four. It is therefore advisable to
use a larger lag interval for computing directional variograms. You should use a lag spacing of 25 to compute the four
directional variograms listed above, superimposing the omnidirectional exponential model on the plot Run the option
sequence below four times, changing only the direction angle. Figures 4-16 through 4-19 display the directional
variograms for 0,45,90, and 135 degrees.
OPTION
ACTION
FIELD
VALUE
QUIT
QUIT
DIRECTION
EXECUTE
MODEL
PLOT
Input
Input
Accept
Direction
Tolerance
Bandwidth
0
22.5
MAX
Geo-EAS 1.2.1
4-11
March 1991
-------
v?Vy" f ' ft f f /
' ^ t t f V,Sr * ' ' '
"/'..",' t's 'ft";, "' ••
'ft;', ,&, s , , , ,, '
^"' ',"*''/, ' - '
f,f $ V&'s
Fll. :«€U.POf
Pain : 428
Dirrct.: .eee
Toi. : 22.sea
Ctdniun Linlls
Htninun: .BOO
Itoxinun: 14.780
Itein : 7,889
88. 120.
5 M.
Vtrloqrtn For Cadniun
File :«xanpl*.poF
Pain : 358
Dir«t.: 49.MM
Toi. : 22.see
HaxBand: n/a
Cadniun Linitl
Hinlnun: .888
Haxlnun: 14.788
Vir. : 15JT1
e 120.
Distknc*
liO. 2BB.
"y<
v//'
4*
&
VATiograH For
FiU !«x«npl«.pof
Pairs : 344
oir.ot.: ra.eee
toi. ; 22.see
HaxBand! n/a
Cadniin Llnits
Haxinun: 14.788
B. 128.
Dixtano*
140. 200.
Nun
Var.
7.883
IS. 273
Geo-EAS 1.2.1
4-12
Tutorial
-------
Vtriogr*n for Cadniun
38.
25.
2B.
13.
IB.
3.
Pair*
Dir»ol.
Tol.
Mtxfiand
Cufalun
Hlnii
Haximw
135.eee
22.see
u. roe
7.885
a. 128.
Distinct
These four variograms provide a good illustration of why you usually model the omnidirectional variogram first. In the
directional variograms, most of the definition of shape, nugget, and sill has been obscured. You can see, however, a
general confirmation of the assumption about the anisotropy. The points on the 0 degree variogram all fall below the
omnidirectional model, suggesting the range in that direction should be longer. The opposite is true for the 90 degree
variogram, while the 45 and 135 degree variograms are reasonably well fitted by the omnidirectional model. Obviously,
one cannot be too precise about fitting ranges to these directional variograms. Likewise, it would not be worthwhile to
attempt a more precise definition of the direction of maximum and minimum range.
The program Krige assumes that the directional variogram model ranges form an elliptical pattern. It is therefore only
necessary to fit models to the major and minor axis directions to define the entire 2-D structure. One could make a case
for the range of the major axis (0 degrees) of the exponential model being anywhere between 250 and 400 units, and the
minor axis (90 degrees) being between 60 and 120 units. We will settle on a model with major and minor axes of 300
and 100 units, respectively, and move on to kriging.
A note on alternate types of variograms — The Type option on the Variogram Results screen allows you to select and
plot any of three alternate estimators of spatial variability. These are sometimes less sensitive to outliers, skewed
distributions, or clustered data than ordinary variograms and may help you recognize a structure when the ordinary
variogram is too noisy. The relative variogram is analogous to the relative standard deviation often used to measure
analytical variability. The "madogram" plots the mean absolute differences. The non-ergodic variogram is a relatively
new method (Srivastiva, 1987) based on estimates of covariance rather than variance. Non-ergodic variograms have the
same units (measurement units squared) as ordinary variograms and may be modeled and used for kriging in the same
way. Relative variograms are unitless (decimal fraction squares). When modeled and used for kriging the relative kriging
standard deviations must be multiplied by the estimated values to be comparable with kriging standard deviations
produced with ordinary variogram models. Madograms are not "true variograms" because they are not based upon
squared differences. In general, kriging with madogram models is not recommended.
4.4 KRIGING AND CONTOURING
The program Krige produces a regular grid of interpolated point or block estimates using either "Ordinary" or "Simple"
kriging. The default option, ordinary block kriging, is recommended for most environmental applications. Point kriging
usually provides estimates very similar to those from block kriging, but if a point being estimated happens to coincide
with a sampled location, the estimate is set equal to the sample value. This is not appropriate for contour mapping, which
implicitly requires a spatial estimator. Ordinary kriging estimates the point or block values with a weighted average of
the sample values within a local search neighborhood, or ellipse, centered on the point or block. Simple kriging also
assigns a weight to the population mean, and is in effect making a strong assumption that the mean value is constant over
the site; it also requires that the available data be adequate to provide a good estimate of the mean.
In order to execute Krige we must provide the names of the data file and an output grid file, and we must select a variable
and enter a variogram model. The program computes a default lOx 10 grid, which we will usually want to override with
more convenient "round" numbers. The default search ellipse is a circle with a radius about one fourth the maximum
x or y dimension of the site, which should be adequate for most cases. The purpose of the search is to reduce computation
time by eliminating from the kriging system of equations those samples which are unlikely to get "significant weights".
The default search strategy is to treat the search circle as a single "sector", to examine all samples within it and use at
Geo-EAS 1.2.1
4-13
March 1991
-------
least one, but not more than the closest eight. The number of samples required for kriging is related to the value of the
nugget term in the variogram compared to the maximum variogram value possible within the search area. The higher
the nugget, the more likely that more distant samples will get significant weights. A rough rule of thumb would be to use
eight samples when the nugget is near zero, increasing to twenty when the nugget is more than 50% of the maximum
value. The more complex sector search options may be useful when you have unusual patterns or clusters of data. We
will accept the default search for now, and check during kriging to see how well it works. Initiate program Krige, and
the main screen will be displayed (Figure 4-20).
The Krige main menu allows you to retrieve previously saved kriging parameters, or to save the parameters you have
just used before exiting the program. Because this is your first attempt with this data set, you must use the Options/
Execute option to go directly to the Options screen and menu. This screen is displayed in Figure 4-21.
A program far kriging a grid of estimates
File Prefix: C:\GeoEAS\Data\
Head Parameter File
Input
Parameter Pile:
Saue Parameter File
Output
Parameter File:
Prefix
Use this option to enter « prefix
which is used to build file nones
used by the program.
Read Parameters Options/Execute Saue Parameters Quit
Enter the Prefix for files
Figure 4-21
U -•:•:»>• *ViV*Hii:B*- — |
Title: Example. grd - kriged estimates of data fron Exanplc.dat
Data
Data File : Example.dat
Output File : Example. grd
Polygon
Polygon File:
Sanple Select: Ha
Type
Type of Kriging : Ordinary
Point or Block : Block ZxZ
Grid Parameters
X
Variable : Easting
Origin : 268. 808
Spacing : 28.800
Number : 13
Search Parameters
Major Badius :
Minor Radius :
Ellipse Angle:
Distance Type: Euclidean
*
Northing
128.806
20.906
11
1 Sectors : 1
Nax in Sector: 16
Nin. to use : 8
Empty Sectors: «
Data Polygon Type Grid Search JCT8HJiH3HiBEEIH Title Execute Quit
This option Invokes the Variables and Variogran Models screen
Geo-EAS 1.2.1
4-14
Tutorial
-------
Use the following option sequence to specify the file names and grid parameters, and to proceed to the next menu (Figure
4-22):
OPTION
ACTION
FIELD
VALUE
OPTIONS/EXECUTE
DATA
GRID
Accept
Accept
Accept
Accept
Input
Input
Input
Input
Input
Input
Data File
Grid File
X variable
Y variable
X origin
Y origin
X cell size
Y cell size
X # cells
Y # cells
Example.dat
Example.grd
Easting
Northing
260
120
20
20
13
11
VARIABLES/MODELS
odels Screen
List
of
Variables
to
Krige
1 Cadniun 3
2
3
4
6
B
3
10
BHlWWiWIlMHri-rti-Hti-ll
Variable : Cadniun Global Hean
Variogran Model Parameters
Nugget : 4.566
1 Type Sill Ualue flajor Range Hi nor Range Angle
1 Exponent. 13.590 300.000 160.000 60
Z
3
Edit Delete Quit
MA a new variable and Model to the Kriging List
The following option sequence selects Cadmium as the variable to be kriged, enters the variogram model, executes the
kriging routine, and saves the parameter file:
OPTION
ACTION
FIELD
VALUE
NEW VARIABLE
QUIT
EXECUTE
QUIT
SAVE PARAM.
Toggle
Input
Toggle
Input
Input
Input
Accept
Accept
Variable
Nugget
Type
Sill value
Major range
Minor range
Angle
Parameter file
Cadmium
4.5
Exponential
13.5
300
100
0
Example.kpf
Upon selection of the Execute option, the program first displays a color-coded sample location map on the screen, and
then overlays this with a color-coded/shaded grid cell as each kriged estimate is computed. At the bottom of the screen,
a summary line for each estimate is displayed. As you watch this proceed, you may note that the number of samples being
used is only less than the specified 8 for the exterior blocks of the grid, indicating that the default search radii are adequate
to obtain 8 neighbors. You can use the "debug" options during the kriging computations to help you understand what
is actually happening in the program, and to decide whether you need to change the search options. Activating provides you with a map showing the search ellipse and the samples selected for kriging the current block. The
Geo-EAS 1.2.1
4-15
March 1991
-------
goal of the search is to include all of the samples which are relevant to the estimate, while avoiding spending a lot of time
computing negligible weights for samples that do not matter. The key lets you look at a list of the selected
samples' coordinates, distances from the block center, and kriging weights. Use to continue to subsequent
displays.
e
Given that sample weights must sum to 1.0, it seems reasonable to conclude that samples with weights of less than 0.01
can be neglected without significantly affecting the kriging results. The goal of your search would therefore be to
consistently find a set of samples such that the lowest two or three weights would be at or just below 0.01. When you
examine the lists of weights for a number of blocks during this run, you find the lowest weights to generally be in the
range of 0.02 or 0.03. This is not really bad, but it might have been better to raise the maximum number of samples to
10 or 15 (and increase the search radii, if necessary).
The kriged results have been written to the file Example, grd. Proceed to contour this grid of kriged values using the
program Conrec. First initiate Conrec, and use the following option sequence. The resulting graph is displayed in Figure
4-23.
OPTION ACTION FIELD
VALUE
OPTIONS/EXECUTE
DATA Accept
Accept
Accept
Accept
Answer
EXECUTE Accept
Data File
X variable
Y variable
Contour variable
Metafile
Example.grd
Easting
Northing
*Cadmium
Y
Metacode.met
QUIT
Contours for
Estimates
' 3 r :*, *
, / .', ,,
The final option sequence below plots a contour map of the kriging standard deviations or estimation errors (Figure 4-
24), and demonstrates some of the options in Conrec:
OPTION ACTION FIELD
VALUE
OPTIONS/EXECUTE
VARIABLES Accept
Accept
Toggle
Answer
CONTOUR OPTIONS
NEW LEVELS Accept
Accept
Input
X variable
Y variable
Contour variable
Starting Value
Maximum Value
Cont. Increment
Easting
Northing
KSDCadmium
Y
1
3
0.25
Geo-EAS 7.2.7
4-16
Tutorial
-------
DASH PATTERN
QUIT
EXECUTE
Input
Input
Accept
Accept
QUIT
QUIT
Dash Pattern
Dash Cutoff
# Rep/Label
Metafile
1.9
5
Metacode.met
Krtglng emtirnatom produced from oata ftM axampii grd
Contour! for KSDCadmtum
a*o. -^
;w-- L*S^>-
" L ^^=-~ - -.ISQDOfcJ-Ol
"* -^ — •" ~ •**. "^ f
IPO. 100. 340. MO. 420. 4M
'S *' 'J. V»
? ",„„, '' ,' '
4f
This map illustrates the reasonable result that the highest kriging errors are predicted in areas with the lowest density of
sample data.
4.5 SUMMARY AND EXERCISES
The example exercise just completed contained the basic elements of any geostatistical study. You started with a sample
data set, conducted an exploratory statistical analysis, interpreted the spatial correlation structure of the data and inferred
an underlying variogram model, and used the model to interpolate a grid of kriged estimates. In the process you had to
make a number of "judgment calls" which affected the results. You treated the data set as representing a single
population. You chose not to delete any outliers. You chose to represent the spatial correlation structure of the data with
an anisotropic exponential model plus a nugget term. You accepted the default kriging option of ordinary block kriging
(with blocks approximated by a 2x2 grid of points). Finally, a conclusion was drawn that the default maximum of 8
samples in the kriging program should be increased.
Readers with little or no previous experience in geostatistical analysis may not feel comfortable with this entire process.
It is not always obvious which of these factors are most significant and which if any can be ignored. Nor is it easy to
define the point at which to conclude that you have done the best you can, given the quality and quantity of data. The
best remedy for this situation is practice: Rerun KRIGE with Example.dat, using various combinations of the variogram
model, search strategy, kriging type, grid size, etc., until you get a feel for how these factors interact. The two exercises
below suggest ways of comparing the results from different kriging options, and also utilize some of the other Geo-EAS
programs.
EXERCISE 1 - Compare Anisotropic vs. Isotropic variograms
Step 1. Run Trans to read Example.dat and write a new file named Compare.dat. Use the Create option to create
a new variable Cdl equal to the old variable Cadmium (by adding a constant 0 to the variable Cadmium).
This step will help to avoid the problem of creating two kriged variables with the same name. Repeat the
process for another new variable Cd2. Delete the variables Arsenic, Cadmium, and Lead, and save the
result in Compare.dat.
Step 2. Run Krige with the data file Compare.dat to create a file of kriged estimates called Compare.grd. Krige
both variables Cdl and Cd2 in the same run. Krige Cdl with the anisotropic exponential variogram model
you just used in the example. Krige Cd2 with the equivalent isotropic model (major and minor ranges both
equal 160).
Geo-EAS 1.2.1
4-17
March 1991
-------
Step 3. Run Trans with the grid file Compare.grd to create a new variable called *Cd 1 -*Cd2. Save the results back
into Compare.grd.
Step 4. Run Conrec with the grid file Compare.grd to plot contour maps of *Cdl, *Cd2, and *Cdl-*Cd2.
Step 5. Run Scatter with the grid file Compare.grd to plot *Cdl vs. *Cd2.
Step 6. Run Stall with the grid file Compare.grd to plot histograms of *Cdl, *Cd2, and *Cdl-*Cd2.
EXERCISE 2 - Compare Point vs. Block kriging
Step 1. Run Krige with the data file Compare.grd to create a grid file of kriged estimates called Comp 1 .grd. Use
the isotropic exponential model, and krige Cdl with ordinary point kriging.
Step 2. Repeat Step 1 with a grid file called Comp2.grd. Krige Cd2 with ordinary block kriging (2x2), keeping
all other parameters the same.
Step 3. Run Dataprep to merge Comp2.grd into Compl.grd.
Step 4. Repeat Steps 3-6 from Exercise 1, using Compl.grd
These exercises can be repeated to make other interesting comparisons. For example, compare the results of kriging with
a variogram model consisting of only a nugget term vs. a spherical or exponential model with zero nugget. Or compare
kriging with a maximum of 4 samples vs. 20 samples, all other parameters being equal.
Geo-EAS 1.2.1 4-18 Tutorial
-------
SECTION 5 DATAPREP
5.1 WHAT DATAPREP DOES
Dataprep provides utilities for Geo-EAS data files. Dataprep has two divisions, the DOS Utilities and the File Operations.
The DOS Utilities allows access to commonly used DOS commands. The File Operations include utilities to manipulate
Geo-EAS data files.
The Dataprep File Operations use temporary files called Scratch Files for storing data read from a Geo-EAS data file and
for processing. The Append and Merge operations require an additional temporary file for processing. The temporary
files are called ZZSCTCH1.FIL and ZZSCTCH2.FIL. Each time an operation is executed the temporary files are
generated and then deleted after processing is complete.
5.2 DATA LIMITS
Dataprep reads and generates Geo-EAS data files containing a maximum of 48 variables and 10,000 samples. If a file
should contain more than 10,000 samples then only the first 10,000 samples are read and a warning message is displayed.
The file operations will generate output data files containing up to 10,000 samples. If a file operation should generate
an output data file requiring more than 10,000 samples then only the first 10,000 samples are written. In such a case no
warning messages are displayed.
5.3 THE MENU HIERARCHY
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Geo-EAS 1.2.1 5-7 March 1991
-------
5.4 THE MAIN MENU
DATA PREPARATIOH (I.Z.I)
Data File Prefix :
Scratch File Prefix:
C:\GeoEASsDataS
DESCRIPTION:
This option displays file operations along uith a
narrative describing each choice. These operations
are: append, colunn(uarlable) extract, rou extract,
conpress, ID var, merge, report and sort.
These operations can produce output files with a
naxlmin of 48 variables and 10,000 records.
If you wish to use one of these operations or require
•tore Information on a specific operation then press
.
Prefix DOS Utilities
Quit
The Main screen and menu (Figure 5-1) provides options which allow you to access the DOS Utilities and File Operations
menus. The menu line appears as follows:
Prefix DOS Utilities File Operations Quit
Prefix
The Prefix option is used to enter the prefix strings for (he data file and the scratch file.
DOS Utilities
The DOS Utilities option provides access to the DOS Utilities menu. The DOS Utilities menu provides access to the DOS
commands such as Directory, Print, List (same as the DOS "MORE" command), Copy, Rename, and Delete. Refer to
your DOS manual for further information on these DOS commands. The DOS Utilities menu is discussed below.
File Operations
The File Operations option provides access to the File Operations menu. The File Operations menu provides the
following file operations: Append, Column (variable) extract, Row extract, Compress, ID Variable, Merge, Report and
Sort. The File Operations menu is discussed below.
Geo-EAS 1.2.1
5-2
Dataprep
-------
5.5 THE DOS UTILITIES MENU
Scratch File Prefix:
DOS UTILITIES:
IlllllillllllUII
Print
List
Copy
Renane
Delete
DOS Comand
Quit
The directory
specified uill be
displayed. You will be prompted for
the directory
if any. Upon
directory will
screen . Press
including the prefix.
execution that
be displayed on the
The DOS Utilities screen and menu (Figure 5-2) provides commonly used DOS commands. These commands operate
just as the DOS commands do. Refer to your DOS manual for further information. To select an option from the vertical
menu, use the or arrow key (not the or arrow key) to position the cursor bar then press the
key.
Directory
Upon selection of this option the Directory menu is displayed. The Directory menu provides the options necessary to
list all directory entries or only those for specified files. The directory option is similar to the DOS command "Dir". The
menu line appears as follows:
Directory Execute
Directory This option results in a prompt for a character string. The string can be either a directory or
file name. The string is entered into an alphanumeric field that is 55 characters long. If the
field is left blank then the current directory is used by default.
Execut Selection of this option causes the directory to be displayed on a new screen. An error
message appears if the directory is non-existent. After the directory is listed the message
"Press to return to menu" is displayed. The key returns control to the
Directory menu.
Print
Upon selection of this option the Print menu is displayed. The Print menu provides the options necessary to print a file.
The Print option is similar to the DOS command "Print". The menu line appears as follows:
Files Execute Quit
Files Upon selecting this option, you are prompted for the name of the file that is to be printed.
Execute Selection of this option causes the specified file to be printed. A yes/no prompt appears asking
if the printer is ready. If yes is indicated then the DOS Print command is executed. When
printing begins the Print menu screen is displayed and a message appears indicating that the
file is being printed.
List
Upon selection of this option the List menu is displayed. The List menu provides the options necessary to list a file. The
List option is similar to the DOS command "More". The menu line appears as follows:
File Execute Quit
Geo-EAS 1.2.1
5-3
March 1991
-------
File You will be prompted for the name of the file that is to be listed.
Execute Upon selection of this option DOS executes the "More" command. The screen is cleared and
the contents of the file are displayed. When the screen is filled the message "More" appears
on the last line. The key causes another page of the file's contents to be displayed.
After the entire file has been listed, press to display the List menu screen and control
is returned to the List menu.
Copy
Upon selection of this option the Copy menu is displayed. The Copy menu provides the options necessary to copy a file.
The menu line appears as follows:
Files Execute Quit
Files You are prompted for two file names. Upon execution, the contents of the first data file are
copied over to the second data file.
Execute Upon selection of this option DOS executes the "Copy" command. When the file has been
copied a message is displayed. An error message appears whenever the "Copy " command
could not be successfully executed.
Rename
Upon selection of this option the Rename menu is displayed. The Rename menu provides the options necessary to rename
a file. The menu line appears as follows:
Files Execute Quit
Files You are prompted for two file names. The name of the file specified first is renamed to the
second file name given. If a data file exists with the second file name, then an error message
appears.
Execute Upon selection of this option, DOS executes the "Rename" command. A message stating that
the file has been renamed appears after the process is complete.
Delete
Upon selection of this option the Delete menu will be displayed. The Delete option uses the DOS command "Del". The
menu line appears as follows:
File Execute Quit
File You will be prompted for the name of the file to be deleted.
Execute Upon selection of this option, DOS executes the "Delete" command. After the file has been
deleted an informative message is displayed.
DOS Command
Upon selection of this option you will access DOS. To return to Dataprep type the command "Exit ".
Geo-EAS 1.2.1 5-4 Dataprep
-------
5.6 THE FILE OPERATIONS MENU
Operation^ Screen
Data File Prefix : CAGcoEftSSDataV
Scratch File Prefix:
FILE OPTIONS:
Append
Colunn Extract
lilMtSHTgm
Conpress
ID variable
Merge
Report
Sort
Quit
Rows of data> ie. sanplesj are extracted
fron an input file based upon a logical
expression and written to an output
file. The first operand is « variable
and the second operand can be either a
variable or a constant. The logical
relations arc: .LT., .LE. , .GT. , .GE.,
.EQ...MI..
The data file prefix noted above will
precede the f i les . Press
The File Operations screen and menu (Figure 5-3) provides a set of useful operations for manipulating Geo-EAS data
files. To select an option from the vertical menu, use or (not or ) to position the cursor,
and press to select the option. The two Gco-EAS input data files called Demol .dat and Demo2.dat are used to
demonstrate each file operation discussed below.
Demol.dat - ficticious data
3
Easting
Northing
Arsenic
320.0
119.0
115.0
114.0
114.0
431.0
feet
feet
ppm
Demo2.dat - ficticious data
3
Easting
Northing
Lead
102.0
122.0
116.0
150.0
148.0
feet
feet
ppm
set!
311.0
119.0
111.0
269.0
269.0
137.0
set 2
164.0
137.0
119.0
315.0
291.0
.850
.630
.560
1.020
1.020
.67
.300
.360
.700
.500
.710
Append
Upon selection of this option the Append menu will be displayed. The Append menu provides the options necessary to
append two Geo- EAS data files. A discussion on the append operation follows in the Execute option. The menu line
appears as follows:
Files
Files Execute Quit
You are prompted for three Geo-EAS data file names. Upon execution the second file name
specified is appended to the first file name entered. The first and second file names cannot
be the same. If they are then an error message appears. The third file name entered is the name
of the output file.
Geo-EAS 1.2.1
5-5
March 1991
-------
Execute Upon selection of this option, Dataprep will append the second file to the first file and store
the results in the output file. After the operation is complete the output variables are displayed
on the screen and a message is displayed. Upon pressing any key, control is returned to the
Append menu. A discussion of the Append operation follows:
Assume the first input file will be called Filel and the second input file called File2. Variables
that exist in both input files (i.e. have identical variable names) will be combined into one
variable with the records of Filel preceding those of File2. The difference is that for Filel
variables the records normally occupied by File2 variables are filled with missing
values(l.E+31). For File2 variables the records normally occupied by Filel variables are
filled with missing values. As an example the output file Outl.dat was generated when
Demol.dat (above) as Filel and Demo2.dat (above) as File2 were appended. Outl.dat is
shown below.
Outl.dat
Demol.dat - ficticious data set 1
4
Easting feet
Northing feet
Arsenic
Lead
320.0
119.0
115.0
114.0
114.0
431.0
102.0
122.0
116.0
150.0
148.0
ppm
ppm
311.0
119.0
111.0
269.0
269.0
137.0
164.0
137.0
119.0
315.0
291.0
.850
.630
.560
1.02
1.02
.670
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.10E+32
.300
.360
.700
.500
.710
Column Extract
Upon selection of this option the Column Extract menu is displayed. The Column Extract menu provides the options
necessary to create a Geo-EAS data file with variables extracted from an input file. The menu line appears as follows:
Files
Variables
Execute
Files Variables Execute Quit
This option is used to specify two file names. The first, an input file, is a Geo-EAS data file.
The second file is a Geo-EAS output file.
This option is used to specify one or more variables which will be extracted and written to
the output file when the Execute option is selected. The variables are selected from a toggle
field. After each selection, the variable name is displayed on the screen and a yes/no prompt
appears asking if you wan t to select another variable. If yes is indicated then you are prompted
for another variable. If no is indicated then control is returned to the Column Extract menu.
Upon selection of this option, the selected variables and related data are copied and stored
in the output file. When the operation is complete, a message is displayed. Upon pressing any
key, control is returned to the Column Extract menu.
Row Extract
Upon selection of this option the Row Extract menu is displayed. The Row Extract menu provides the options necessary
to perform row extraction. This operation extracts samples from the specified input Geo-EAS data file based upon a test
condition. The menu line appears as follows:
Files
Subsetting Condition
Files Subsetting Condition Execute Quit
This option is used to specify two files. The name of first file entered, an input file, is a Geo-
EAS data file. The name of the second file entered is an output file.
This option is used to specify a test condition. The test condition is of the form , where <0perand 1> is a variable and can be a variable
or a constant. can be:
Geo-EAS 1.2.1
5-6
Dataprep
-------
.LT., .LE. Less than, Less than or equal to
.GT., .GE. Grater than, Greater than or equal to
.EQ., .NE. Equal to, Not equal to
Upon selection of the Subsetting Condition option the variable names stored in the input file
are displayed. You are prompted for a variable for the Operandl from a toggle field. After
the selection you are prompted for a logical operator from the toggle field. After this
selection, control is passed to the Row Extract Operand menu. The Row Extract Operand
menu is the next menu discussed. After a selection is made for the second operand, control
is returned to the Row Extract menu.
The Row Extract Operand menu provides the options necessary to select a variable or enter
a constant for Operand2. The menu line appears as follows:
Constant Variable
Constant This option is used to specify a constant(floating point) number for Operand2. The constant
is entered into a numeric field. If a constant causes a numeric overflow, then a message
appears informing you of the error (pressing any key returns control to the Row Extract
Operand menu). After a valid constant has been entered, pressing returns control to
the Row Extract menu.
Variable This option is used to specify a variable for the Operand2. The variable is selected from a
toggle field. After the selection, pressing returns control to the Row Extract menu.
Execute When selecting the Execute option, the Row Extraction process is initiated. Each sample of
Operandl, described above, is checked to see if it satisfies the test condition. If so then that
entire line of data is extracted from the input data file and stored in a temporary file. After
this process is complete, the data from the temporary file are stored in the output file. When
the data have been stored to the output file and the execution complete, you are informed with
a message stating that the data has been sent to the output file. If no samples satisfy the test
condition, then a message appears and no data are stored. In both cases, pressing any key
returns control to the Row Extract menu.
As an example of the Row Extraction operation, the following output data file, Out2.dat, is
generated when Demol .dat is the specified input file and the test condition is: Easting .LE.
Northing.
Out2.dat
Demol.dat - ficticious data set 1
3
Easting
Northing
Arsenic
119.0
114.0
114.0
feet
feet
ppm
119.0
269.0
269.0
.630
1.02
1.02
Compress
Each data record in Demo 1 .dat is examined by the program. If the test condition is true, then
that line in the file is extracted and stored in the specified output file. Only those records
satisfying the specified logical expression will be extracted and stored in the output file.
Upon selection of this option the Compress menu is displayed. The Compress menu provides the options necessary to
compress a Geo-EAS data file. This operation eliminates any duplicate data records that appear in a specified input Geo-
EAS data file and stores the results in the specified output Geo-EAS data file. An example is shown in the Execute option.
The menu line appears as follows:
Files
Files Execute Quit
This option is used to specify two data file names. The first, an input file, is a Geo-EAS data
file. The second is an output file. After the two files have been specified, the variable names
stored in the input file are displayed.
Geo-EAS 1.2.1
5-7
March 1991
-------
Execute Upon selection of this option, the data from the input file are stored in a temporary file.
Duplicate records are deleted and the data are stored in the specified output file. When the
entire process is complete, a message stating that the data have been sent to the output file
is displayed. Upon pressing any key, control is returned to the Compress menu.
As an example of the Compress operation, the following output file, Out5.dat, was generated
when the input file, Demol.dat, was compressed. Out5.dat follows.
Out5.dat
Demol.dat - ficticious data set 1
3
Easting
Northing
Arsenic
320.0
119.0
115.0
114.0
431.0
feet
feet
ppm
311.0
119.0
111.0
269.0
137.0
.850
.630
.560
1.02
.670
***Note that all duplicate records have been deleted.***
ID Variable
Upon selection of this option the ID Variable menu is displayed. The ID Variable menu provides the options to create
the variable "Sequence #". The Sequence # denotes the sequential position of the data in the input file. An example of
this is shown in the Execute option. The menu line appears as follows:
Files Execute Quit
Files This option is used to specify two Geo-EAS data file names. The first is an input data file.
The second is an output fi le. A fter the two files have been specified, the variable names stored
in the input file are displayed.
Execute This option appends a variable called "Sequence #" to the current listing of variables
displayed on the screen. The variable name "Sequence #" is appended to the variable names
read from the input file. These variable names are then stored in the specified output file. An
example of such an output file is Out6.dat.
Out6.dat
Demol.dat - ficticious data set 1
4
Easting feet
Northing feet
Arsenic ppm
Sequence #
320.0 311.0 .850 1.
119.0 119.0 .630 2.
115.0 111.0 .560 3.
114.0 269.0 1.02 4.
114.0 269.0 1.02 5.
431.0 137.0 .670 6.
Merge
Upon selection of this option the Merge menu is displayed. The Merge menu provides the options necessary to merge
two Geo-EAS data files. The details of this operation are discussed in the Execute option. The menu line appears as
follows:
Files Execute Quit
Files This option is used to specify the names of two Geo- E AS data files which are to be merged,
and the name of an output file, which will contain the results. The files to be merged cannot
have the same file name, or an error message appears.
Geo-EAS 1.2.1 5-8 Dataprep
-------
Execute When this option is selected, the Merge process is initiated. After this process is complete
the variables from the output file are displayed and a message indicating that the data have
been sent to the output file appears. Pressing any key returns control to the Merge menu. To
describe the merge process, assume that Filel is the first file name entered and File2 is the
second file name entered. If one input file is smaller than the other input file, then the smaller
file has missing values added to its variables. Variables that appear in both input Filel and
input File2 are combined with the samples of Filel preceding those of File2. The specified
output file stores the results of the merged files. An example best demonstrates the merge
operation. The output file, Out3.dat, which follows, displays the merging of input files
Demol.dat as Filel and Demo2.dat as File2.
Out3.dat
Demol.dat - ficticious data set 1
4
Easting feet
Northing feet
Arsenic ppm
Lead ppm
320.0
119.0
115.0
114.0
114.0
431.0
311.0
119.0
111.0
269.0
269.0
137.00
.850
.630
.560
1.02
1.020
.6700
.300
.360
.700
.500
.710
1.E31
*** NOTE *** The variables appearing in both input files are combined into one variable (Easting and Northing),
and these variables took on the values from the first file.
Report
Upon selection of this option the Report menu is displayed. The Report menu provides the options necessary to generate
a listing of specified variables in "Report" form. The "Report" listing is described in the Execute option. The menu line
appears as follows:
Files Variables Execute Quit
Files This option is used to specify two file names, the input and output files. After the file names
have been entered, you are prompted for the sequence option from the toggle field. If "on"
is selected for the sequence option, then the observation (row) number is indicated on the
"Report" listing.
Variables This option is used to specify those variables that are to be included in the "Report" listing.
You are prompted for a variable to be selected from a toggle field. A yes/no prompt provides
an opportunity to select another variable. Indicating no causes control to be returned to the
Report menu. The list of variables are displayed on the screen after each selection.
Execute The "Report" listing will be generated upon selection of this option. This listing is then stored
in the specified output file. When this operation is complete a message appears indicating
that the data have been sent to the output file. Upon pressing any key, control is returned to
the Report menu. The following is a description of the "Report" listing.
The "Report" listing can be generated with or without the sequence option enabled. If the
sequence option is enabled then each data record will be preceded by an observation number
(record number). Each page lists up to four variables with 50 data records each. If more than
four variables are selected then all the data records for the first four variables are printed. The
page numbering is reset to one and the next four variables are printed. An example report with
the sequence option enabled follows.
Example output from the Report option:
Page 1
Demol.dat ficticious data set 1
Easting Northing Lead Arsenic
Obs. feet feet ppm ppm
1. 320.0000 311.0000 .8500000 1.000000
Geo-EAS 1.2.1 5-9 March 1991
-------
2. 119.0000 119.0000 .6300000 2.000000
3. 115.0000 111.0000 .5600000 3.000000
Sort
Upon selection of this option the Sort menu is displayed. The Sort menu provides the options necessary to sort a variable
in ascending order. If a selected variable's sample has to be relocated, then the entire record associated with that sample
is also moved. An example of the Sort operation is shown in the Execute option. The menu line appears as follows:
Files Variable Execute Quit
Files This option is used to specify two Geo-EAS file names, the first is the input file and the second
is an output file.
Variable This option is used to specify the variable to be sorted. You are prompted for a variable which
is selected from a toggle field. After the selection, pressing any key returns control to the Sort
menu.
Execute Upon selection of this option, the specified variable is sorted in ascending order. When the
process is complete, the data are stored in the specified output file. A message appears
informing you that the data have been sent to the output file. Upon pressing any key, control
is returned to the Sort menu.
As an example the following output file, Out4.dat, was generated when the variable Easting
of the input file, Demol.dat, was sorted.
Out4.dat
Demol.dat - ficticious data set 1
3
Easting feet
Northing feet
Arsenic ppm
114.0 269.0 1.02
114.0 269.0 1.02
115.0 111.0 .560
119.0 119.0 .630
320.0 311.0 .850
431.0 137.0 .670
The variable Easting appears in ascending order. Note that not only have the values of the variable Easting been relocated,
but all values (the line) associated with Easting has been moved.
Geo-EAS 1.2.1 5-JO Dataprep
-------
SECTION 6 TRANS
6.1 WHAT TRANS DOES
Trans was designed to create, delete, or modify Geo-EAS data file variables. Refer to the section on Geo-EAS data files
for more information on input data. The operations may be unary (one operand, one operator), binary (two operands,
one operator), or a indicator transform operation, described below. An operand may be either a variable or a constant.
The operator maybe an operation, such as addition or finding the square root. The results generated by the specified
operation may replace the contents of an existing variable or a new variable may be created. The variable specified to
accept the results is called the result variable. Missing values may be generated in two circumstances: when an operand
is a missing value, or when an operation is undefined (as in division by zero).
Trans uses a temporary file called a Scratch File to store the data read from a Geo-EAS data file. The temporary file is
called ZZSCTCH1 .FIL. The Read option in the Main menu (described below) reads the Geo-EAS data file and stores
the data in the temporary file. Each time an operation is performed, the required data are retrieved from the temporary
file and the newly generated data are stored in the temporary file. A list of variable names is displayed on the screen to
indicate which variables reside in the scratch file. If a variable is deleted using the Delete option from the Main menu,
then that data are deleted from the temporary file. The variable name is also deleted from the screen. The Save option
from the Main menu is used to move the data from the temporary file to the specified Geo-EAS output data file.
6.2 DATA LIMITS
Trans reads as well as generates Geo-EAS data files containing a maximum of 48 variables and 10,000 samples. If a file
should contain more than 10,000 samples then only the first 10,000 samples are read and a warning message is displayed.
If an attempt is made to create a 49th variable then an error message
is displayed.
6.3 THE MENU HIERARCHY
Trans »«.«««««.»«*—«) fteiix •'''•••• •••;•
I Read ; | . . .
I Titife . ::
\ Create —- ~~ «—: I Ndv Variable —~ I Unary Opeta^oa
I I 014 Variable { Binary Gperaiioft
I ' 1 '•":'••• \ Indicator Transform
I : I - : \ Quit
) A Quit
1 Delete - :
1 Save -.:.,..-. >••::.;
^ <^uif : •"••". ;:. ".-.:V
UnaryjOperalion — -— i Operation — — i Constant -— — t Execute
^ * 1 I Variable V-Q6U'
1 i j*. +
\ Outt : . ; ;
} Copstant ~-» —..I Qp^ration »— *« I Constant ^~«* «« I
1 Variable I ; [ Vaoabfe \ Quit
I I ; . \ Quii
) V Quit
\ Quit i
I Variable ~~ —.— Cutoff :
1 Execute : ....: •, : .
\ Qaii : ;
Geo-EAS 1.2.1 6-1 March 1991
-------
6.4 THE MAIN MENU
! /
Data File Prefix : CAGeoEASsDdUS
Scratch file Prefix:
maam-
Input File: Exanple.dat Output Flic:
Title : Exanple.dat - Geostatistical Enuiromental Assessment Software
Operation
Variables
Easting Northing Arsenic Cadnlun Lead
Prefix lima title Create U_Delete Saue Quit
Vou will be prompted for an input filenane
The Main screen and menu (Figure 6-1) provide the options necessary to read and save Geo-E AS data files and to create,
delete, or modify variables. The menu line appears as follows:
Prefix Read Title Create Delete Save Quit
Prefix
The Prefix option is used to enter the prefix for the data file and scratch file.
Data
The Data option is used to enter the name of a Geo-EAS data file.
Title
The Title option is used to specify a descriptive title for the output Geo-EAS data file. The title can be up to 66
alphanumeric characters. No error checking is performed.
Create
The Create option provides access to the Create menu. The Create menu (described below) is the first in a series of menus
that provide options used to specify a new or existing variable as the result variable and to perform a specified operation
(unary, binary, transform indicator).
Delete
The Delete option is used to select an existing variable that is to be deleted. The variable is selected from a toggle field.
Upon making the selection the message "Do you really want to delete this variable?...(Y/N)" is displayed. If is
pressed the variable is deleted from the temporary file and from the list of variable names on the screen. Subsequent to
entering your choice, control is returned to the Main menu.
Save
When the Save option is selected, the data stored in the temporary file are written to a specified data file. A prompt is
issued for the output Geo-EAS data file name. If blanks arc entered then an error message is displayed. If the output
file already exists then a Yes/No prompt will appear asking if the file should be overwritten. The data in the temporary
file is copied to the output Geo-EAS data file. If an error should occur while opening the output file then an error message
is displayed. While the file is being saved the message "Writing data..." appears. After the data has successfully been
written a message is displayed (press any key to continue).
Geo-EAS 1.2.1
6-2
Trans
-------
6.5 THE CREATE MENU
The Create menu provides the options necessary to perform transformations to a Geo-EAS data file. The menu line
appears as follows:
New Variable Old Variable Quit
New Variable
When the New Variable option is selected a new variable is created in the scratch file. The new variable takes on values
generated from the specified operation (unary, binary, indicator transform). You are prompted for the new variable name.
If the given variable name is blank then a message to this effect appears (pressing any key returns control to the Create
menu). If the variable name already exists then a warning message appears (pressing any key passes control to the
Operation menu). If the variable name is unique to the scratch file then you are prompted for a description of the
measurements. The field for the measurements description can accept up to 10 alphanumeric characters. After entering
the measurements description, control is passed to the Operation menu (described below).
Old Variable
This option is used to specify an existing variable whose contents are replaced by the results of the specified operation
(unary, binary, indicator transform). You are prompted for a variable from the toggle field. After making the selection,
you are asked if you wish to change the variable's current name or measurements description. When indicating yes, you
may retain or change the name by entering up to 10 alphanumeric characters into the field. If blanks are entered then
an error message is displayed (you are then returned to the alphanumeric field and prompted for another variable name).
If the given variable name is the same as the existing variable, then a message appears and you are prompted for a new
variable name. You are then prompted for a measurements description. The measurements description of the old variable
is displayed by default. You may retain or enter another description. Pressing causes the Operation menu
(described below) to be activated.
6.6 THE OPERATION MENU
The Operation menu provides a selection of transformation operations. The menu line appears as follows:
Unary Operation Binary Operation Indicator Transform Quit
Unary Operation
This option provides access to the Unary Operation menu. The Unary Operation menu (described below) is the first of
three menus that provides options needed to complete a unary operation. After a selection is made from one menu, control
is passed to the succeeding menu. The Unary Operation menu provides a selection of unary operators. Next, the Unary
Operand menu provides the choice of a constant or an existing variable for the operand. Finally, the Execute menu
provides the Execute option.
The unary operations perform an operation on one operand. The operations are shown below as they would appear in
the toggle field:
sqrt Computes the square root of an operand.
log Computes the base 10 logarithm of an operand.
In Computes the natural logarithm of an operand.
truncate Truncates the operand.
exp Computes e to the power of x (exp) where e is 2.71828... and x is the operand. Note that a
numeric overflow can result in using the exp operation. In such a case the program will
abnormally terminate (crash).
rank Determines the rank of an existing variable. This operation assigns an integer value to the
result variable based upon the rank of a specified existing variable in a sorted list.
equals Set the variable equal to the operand.
abs. val. Computes the absolute value of the operand.
sign changes the sign of the operand.
The Unary Operation menu provides an option to select a unary operation. The menu line appears as follows:
Operations Quit
Geo-EAS 1.2.1 6-3 March 1991
-------
Operation
This option is used to specify the unary operator. You are prompled for a unary operator from the toggle field. Upon
making the selection, control is passed to the Unary operand menu (described below).
The Unary Operand menu provides the option to select an operand for the unary operation. The menu line
appears as follows:
Constant Variable Quit
Constant
Variable
Execute
This option is used to assign a constant value to the unary operand. You are are prompted
for the constant value. The constant value is entered into a numeric(floating point) field. The
default value is initially zero. If the value entered results in a numeric overflow then a
message is displayed. Upon pressing any key, control is returned to the Unary Operand menu.
If the constant value entered is acceptable then control is passed to the Execute menu
(described below).
This option is used to select an existing variable for use as the unary operand from a toggle
field. Upon making the selection, control is passed to the Execute menu (described below).
The Execute menu provides the option necessary to initiate any unary operation. The menu
line appears as follows:
Execute Quit
This option is used to initiate the unary operation. During processing the message
"Processing data..." is displayed on the screen. After processing is complete the minimum
and maximum values of the variable will be displayed on the message line. After pressing
any key, you are asked for the number of significant digits for the output format. The range
of digits is 1 through 12 inclusive. A FORTRAN format (which is the output format) is
constructed based on the expression Gx + 7.x where x is the digit entered by you, ie.,
significant digits. For example, if 7 is entered then G14.7 is the output format. For more
information on the FORTRAN formats refer to a FORTRAN reference manual. If the digit
for x is outside the acceptable range then 9 will be used by default. If the given format is not
appropriate for writing the variable to the output file then a message is displayed and you are
prompted for a new digit for x. You can best select x by determining (using the minimum
and maximum values displayed on the message line) the maximum number of digits to the
left of the decimal point. Then decide the maximum number of digits to the right of the
decimal point. The sum of the two values is x. Increase the sum by one if the value is negative.
If any missing values are generated then the number of missing values and the name of the
variable are displayed on the screen. After processing is complete, control is returned to the
Main menu. If an operand is a constant and contains a missing value then the result of that
operation will be a missing value.
If the operand is a variable as opposed to a constant, and a sample from that variable results
in an undefined operation, then a missing value is generated. Whenever an error message is
displayed, processing is halted and control is returned to the Operation menu. As noted
previously, the operation (exp) may result in a numeric overflow causing the program to
abnormally terminate (crash).
Binary Operation
This option provides access to the Binary Operation menu. The Binary Operation menu is the first of four menus that
provides options needed to complete a binary operation. After a selection is made from one menu, control is passed to
the succeeding menu. First, the Binary Operand One menu (described below) provides a selection of a constant or an
existing variable for operand one. Second, the Binary Operation menu provides a selection of binary operators. Next,
the Binary Operand Two menu is similar to the Binary Operand One menu with the exception that the selection is for
operand two. Finally, the Execute menu provides the Execute option.
The binary operations perform an operation requiring two operands. The operations are shown below as they would
appear in the toggle field:
+ Addition
/ Division of the first operand by the second operand.
x Multiplication
Subtraction
** Exponentiation which raises the first operand to the power of the second operand.
MAX Determines the maximum value of the operands.
Geo-EAS 1.2.1
6-4
Trans
-------
NUN Determines the minimum value of the operands.
Mean Computes the mean of the operands.
The Binary Operand One menu provides the options to select operandl for the binary operation. The menu line appears
as follows:
Constant
Variable
Operation
Constant
Variable
Execute
Indicator Transform
Constant Variable Quit
This option is used to assign a constant value to the binary operand one. This option is similar
to the constant option noted in the Unary Operand menu section (described earlier). The
exceptions are that the wording in the messages refers to the binary operand one and not the
unary operand, and upon entering a valid constant value, control is passed to the Binary
Operation menu (described below). If the constant value is unacceptable then control is
returned to the Binary Operand one menu.
This option is used to assign an existing variable to the binary operand one. This option is
similar to the variable option noted in the Unary Operand menu section (described earlier).
The exceptions are that the wording refers to binary operand one and not the unary operand,
and upon making the selection, control is passed to the Binary Operation menu (described
below).
The Binary Operation menu provides the option to select a binary operator. The menu line
appears as follows:
Operations Quit
This option is used to specify the binary operator. You are prompted for a binary operator
from a toggle field. Upon making the selection control is passed to the Binary Operand Two
menu (described below).
The Binary Operand Two menu provides the options to select operand2 for the binary
operation. The menu line appears as follows:
Constant Variable Quit
This option is used to specify a constant for the binary operand two. This option is similar
to the binary operand one constant option described previously in the Binary Operand One
menu. The exceptions are that the wording refers to operand two and not operand one, and
upon entering an acceptable value, control is passed to the Execute menu (described below).
This option is used to specify an existing variable for binary operand two. It is similar to the
binary operand one variable option described previously in the Binary Operand One menu.
The exceptions are that the wording refers to operand two and not operand one, and upon
making a selection, control is passed to the Execute menu (described below).
The Execute menu provides the option needed to initiate the binary operation. The menu line
appears as follows:
Execute Quit
This option initiates the binary operation. During processing the message "Processing
data..." is displayed on the screen. The Execute(binary) option causes the same prompts as
in the Execute option of the unary operation. Refer to the Execute option of the Execute menu
discussed previously in the Unary operation section. As noted previously, the operation
exponentiation may result in a numeric overflow causing the program to abnormally
terminate(crash).
The indicator transform is an operation requiring two operands. The first operand is an existing variable and the second
operand is a constant called the threshold value. The result variable takes on the value 1.0 if the input variable is greater
than or equal to the threshold value. The result variable takes on the value 0.0 if the input variable operand is less than
threshold value. The Indicator Transform option provides access to the Indicator Transform menu.
The Indicator Transform menu provides the options to select the operands and to execute the operation. The menu line
appears as follows:
Geo-EAS 1.2.1
6-5
March 1991
-------
Variable Execute Quit
Variable This option is used to specify two operands. The first operand is an existing variable and the
second operand is the threshold value which is a constant. The message "Select variable for
operation (use bar)" prompts for the variable. After selection and pressing
the message "Enter constant value for threshold value" is displayed. If the constant entered
causes numeric overflow then an error message is displayed.
Execute This option is used to initiate the indicator transform operation. During processing the
message "Processing data..." is displayed. If after processing any missing values were
generated then the number of missing values and the variable name are displayed on the
message line. After processing is complete the message "Processing is complete...(press any
key)" is displayed. Upon pressing any key control is returned to the Main menu.
Geo-EAS 1.2.1 6-6 Trans
-------
SECTION 7 STAT1
7.1 WHAT STAT1 DOES
Stall is an interactive program which computes basic univariate statistics and displays histograms or probability plots
for variables in a Geo-EAS data set. Options are available for calculating statistics on the natural log of the selected
variable, for specifying a variable to be used as a "weighting factor", and for performing calculations on subsets of the
input data through the use of upper and lower limits. A "Batch Statistics" option has been included which will produce
a report of statistics for all variables in the specified data file.
7.2 DATA LIMITS
Stall requires that the maximum number of variables in the input data file not exceed 48. The data file may contain up
to 10,000 samples. If the data file contains more than 10,000 samples, then only 10,000 will be used by Stall.
7.3
THE MENU HIERARCHY
Stat!
timhs
.Execute
Batct> Statistics
Probability
Examine.
\ Quit ;
Type
Class Limits
Axes
Titles
Results
View Graph
\ Quit
7.4 THE MAIN MENU
ft progran to conpute unloariate descriptive statistics
File Prefix: C:\GeoEflS\IdU\
File
Data File Name : Exanple.dat
Variable
Variable : Cadniun
Weight : Hone
Log Option : Off
Units
Hininun : .000
Naxinun : 16.700
It Variables : 5
It Data records : 60
It Missing Data : 0 (Z
Execute
Use tills option to conpu
display the statistics.
of additional graphs and
uill be displayed.
Ubs<=e)
te and
A nenu
options
Prefix Data Uariablc Unit* i
Conpute basic descriptive stats.
Biitch Statistics Quit
Geo-EAS 1.2.1
7-1
March 1991
-------
The main menu and screen (Figure 7-1) has options to allow specification of the data file names, the selection of the
variable to be used, the selection of upper and lower limits for the variable, calculation of statistics (univariate), and
generation of a batch statistics report. The menu line appears as follows:
Prefix Data Variable Limits Execute Batch Statistics Quit
Prefix
The prefix option is used to enter the prefix for the data file name.
Data
The Data option is used to enter the name of a Geo-EAS data file.
Variable
The variable option allows the selection of a variable for which univariate statistics are to be generated. The "weighting
factor" variable can be selected at this time. The choices available for variables are the variable names specified in the
data file. The natural log transform may be chosen to compute log statistics. Both the weight and log parameters may
be used simultaneously. The screen fields accessed from this option are:
Variable A toggle field for selecting the variable name whose values are to be used to compute the
univariate statistics. The default value is the first variable in the data set.
Weight A toggle field for selecting an optional variable name whose values are to be used as the
weighting factor. If the weighting factor variable is chosen, then the resulting univariate
statistics are "weighted" (the statistics are calculated for Weight value multiplied by Variable
value). The default weighting factor variable is "None"(in which case the weighting factor
isl).
Log Option A two valued toggle (On/Off) field to enable or disable the Log option. If the Log option is
enabled and a weighting factor variable selected then the statistics are calculated for the
Weight value multiplied by the (natural log of the Variable value). Wheneverthe Log option
is enabled sample values less than or equal to zero are counted but not used in the
computation. The default value is "Off.
Limits
The Limits option allows computation of statistics for a subset of the data which lie between the specified minimum and
maximum sample values. You may specify the upper and lower lim its placed on the values used for computing the basic
statistics.
Minimum A numeric field which contains the lower limit on the sample values used in the computation.
The default value is the minimum value of the selected variable.
Maximum A numeric field which contains the upper limit on the sample values used in the computation.
The default value is the maximum value of the selected variable.
Execute
The Execute option provides access to the Results screen and menu. When the Log option is enabled the number of
samples less than or equal to zero is displayed. If this occurs, pressing any key provides access to the Results screen.
See the section on the Results menu below for more information.
Batch Statistics
The Batch Statistics option allows generation of a report of univariate statistics for all variables in the data set with no
need for interaction. The statistics can be saved to a file or printed. A two valued toggle field ("printer" or "file") is used
to make this selection and appears on the message line. If the selection is "printer" then the printer must be on and "online".
If "file" is selected then you are prompted for a file name. The field accepts up to 14 alphanumeric characters. If the
file exists then a yes/no prompt asks if you wish to overwrite. Indicating no will return you to the menu. If the field is
blank then an error message is displayed. In such a case pressing any key returns you to the Main menu.
*** NOTE *** the file by produced by the Batch Statistics option is not a Geo-EAS data file.
Geo-EAS 1.2.1 7-2 Stall
-------
7.5 THE RESULTS MENU
Data File : CAGeoEftSSDataXExanple.dat
Variable : Codniun
Lower Linlt :
Upper Ll.lt : 16
• Observations 60
t Hissing Data 0
t Retained 60
flean
Uar lance
Sta. Deviation
XCoef. Uariation
Skeyness
Kurtosls
090
70«
Sun of Weights
7.8050 Hininiia Ualue
15.5315 25th Perccntile
3.9410 Median
49.9B09 75th Percent ile
naxinum Ualue
-.1510
Z.4639
69.900*
.0600
5.3000
7.9500
10.8009
16.7000
Probability Plot Exanine Quit
Choose histogram parameters / display graph
?''^;:-S,/;^ '
The Results screen and menu provides options to display a probability plot (described below), to display a ranked listing
of data values and order statistics (shown below as "Exam ine Data"), and to display the Histogram screen and menu. The
Results Screen displays univariate statistics for the selected variable. The menu line appears as follows:
Histogram Probability Plot Examine Quit
Histogram
The Histogram option provides access to the Histogram screen and menu. First a default histogram is displayed. See
the section on the Histogram menu below for more information.
Probability Plot
When the Probability Plot option is selected a probability plot (Figure 7-3) is computed and displayed on the screen. The
plot is a graph of the ranked variable values, plotted against their cumulative percentiles. The vertical axis is scaled in
units of the variable and the horizontal axis is scaled in units of cumulative percent. A. boxplot appears at the right side
of the plot area along with univariate statistics, the quartiles, and the minimum and maximum values.
Htstggran
Data file: exanple.dat
1 1 J 1 i
t.
t.
k
3.
e.
a
1
1 — 1 r~
—
— i
~
-
h
4. 8. 12.
Cadniun (ppn)
rn
n
Statistics
N Total : 60
N Hiss : 0
N Used : i»
(lean : 7.883
Variance: IS. 531
Std. Dev: 3.741
•/. Coef .Var: 49.781
Skeunen: -.151
Kurtosis: 2.444
Hininun ,808
25th X : 3.308
Hedian : 7.758
751 h X : 11.800
Naxinun : 14.706
16. 28.
' *' '<
,>' > '\ '''«->''
< 5
Geo-EAS 1.2.1
7-3
March 1991
-------
The boxplot (Figure 7-4) is a graph which depicts the limits, quartiles, median, and mean of a set of values. Boxplots
are used in the Probability Plot and Histogram displays. A Boxplot is comprised of a rectangle containing an "X" and
a dividing line. A line extends outward from each end of the rectangle. The rectangle represents the interquartile range
(the range of values between the 1st and 3rd quartiles). The dividing line marks the position of the median in die
interquartile range, and the "X" marks the arithmetic mean. The endpoints of the outward extending lines depict the
minimum and the maximum values.
Examine
t&e Components
Minimum
1
1 ,.
1
Components of a
Median
1st Quartile Mean
1 ll
V
1 1 1 1 1 1 1 1 1 1
10 20 30 40 50
t
Scale
BOXPLOT
Maximum
3rd Quartile
1 1
1
1
1 1 1 1 1 1 1
60 70 80 90
The Examine option allows access to a screen that displays a ranked listing of data values and order statistics. An example
of this screen is displayed in Figure 7-5. The RecNo column indicates the samples sequence in the data file. The ,
, , , , and keys may be used to scroll the display to the desired position. Pressing
will cause the Results screen and menu to appear.
Hank
1
2
3
1
5
6
7
8
g
16
11
12
13
11
15
16
Data Ualue
.0000
.0000
.9000
1 2000
1.2000
1.6000
1.7000
3.2000
3.1000
3.8000
3.9000
1.0000
1.1000
5. ZOOO
5.3000
5.5000
Height Cur., x
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1 .0000
1.0000
1.0000
i.oooo
1.0000
1.0000
1.0000
i.oooo
• isc t or t to scroll I <1> thru <9> to unsition
eoe
825
612
050
OVS
092
108
125
112
158
175
192
200
ZZS
212
258
or
Probit
-E.391
-1.960
-1.732
-1.5G9
-1.140
-1.331
-1.236
-1 . 150
-1.073
-1.001
-.935
-.872
-.BIZ
-.755
-.701
-.61B
uit
RecMo
30
20
29
31
32
15
33
31
17
39
11
22
13
9
21
21
Geo-EAS 1.2.1
7-4
Stall
-------
7.6
THE HISTOGRAM OPTIONS MENU
Stall Histogram
M
Data File
Variable
Lower Li.lt
Upper Unit
Type
Class Units
HlnlMun
Class Width
1 Classes
Hain title
Sub Title
X Axle
V Axle
C:sGeoEASsData\E»inp]e.<]at
Cadnlun
.000
16.700
Absolute
.000
1.000
20
Axes
Mi ill nun : .030 .060
Ibxinun : 20.080 8.750
Tic Spacing : 1.000 3.0(10
Histogram
Data file: Exanple.dat
Cadnlun (ppn)
Frequency
Type Class Limits Axes Titles Results MljIMdlHIHI Quit
Uieu the histogran as a graph
The Histogram Options screen and menu (Figure 7-6) provides the options necessary to generate a histogram (frequency
distribution plot) of the data. You can examine the histogram results or view the graph. A histogram is displayed before
the Histogram menu is accessed. Pressing any key will access the Histogram menu from the histogram display. The
histogram plot is discussed below in the View Graph option of the Histogram menu. The menu line appears as follows:
Type Class Limits Axes Titles Results View Graph Quit
Type
The Type option is used to select the Frequency type. The Frequency type is selected from a two valued toggle field
containing the choices "Absolute" and "Relative". The choice "Absolute" will generate a traditional histogram;
"Relative" will cause the frequencies to be displayed as a percentage of the total number of samples (or weight of the
samples) retained.
Class Limits
The Class Limits option allows the specification of the class upper and lower limits. You will be prompted for the
minimum value, the class width, and the number of classes. The upper limit of the first class is the sum of the minimum
value and the class width. The upper limit for all classes is the sum of the minimum value and (class width multiplied
by the number of classes). The screen fields accessed from this option are:
Minimum A numeric field whose default value is the minimum value which was specified in the Limits
option of the Main menu discussed earlier.
Class Width A numeric field whose default value is calculated. This value must be greater than zero. If
it is not then an error message appears and you are prompted for a new value.
# Classes A numeric field for which the value entered must be in the range of 1 to 100. If the entry is
erroneous then an error message appears and the default value is set to 100.
Axes
The Axes option allows the specification of the coordinate limits for the horizontal (X) and vertical (Y) axes. Tic spacing
for the X and Y axes is also specified at this time. The screen fields accessed from this option are:
Minimum Two numeric fields used for entering the minimum coordinate values to be used on the X and
Y axes. The default value for X is determined from the data file for the variable for which
univariate statistics are computed and from the upper and lower class limits. The default
value for Y is zero.
Geo-EAS 1.2.1
7-5
March 1991
-------
Maximum Two numeric fields used for entering the maximum coordinate values to be used on the X and
Y axes. If the maximum value exceeds the minimum value then an error message is displayed
and the default value is the previous field entry. The default values displayed are determined
from the data file for the variable for which univariate statistics are computed and from the
upper and lower class limits.
Tic Spacing Two numeric fields used for entering the tic spacing to be used on the X and Y axes. The
default values displayed are determined from the data file for the variable for which
univariate statistics are computed and from the upper and lower class limits.
Titles
The Titles option allows you to enter the title and labels for the graph. The Hershy character sets of 33 fonts are used
for plotting alphanumeric labels. The file HERSHY.B AR contains this information and is included with the software.
Main Title An alphanumeric field which may contain up to 60 characters for the title on the graph. The
default title is "Histogram". When a weighting factor has been selected then the title is
"Weighted Histogram".
Subtitle An alphanumeric field which may contain up to 60 characters for the subtitle of the graph.
The default sub- title is "Data file: ".
X Axis Analphanumericfieldwhichmaycontainupto60charactersfortheXaxis. The default label
is " ()" where the variable name and the measurements
description are taken from the variable selected for univariate statistics. If the Log option
is on then "LN" precedes the variable name.
Y Axis Analphanumericfieldwhichmaycontainupto60charactersfortheYaxis. The default label
is "Frequency".
Results
The Results option allows access to the Histogram Results screen and menu (Figure 7-7). This screen displays the
histogram results. The results are in tabular form. The display
may be scrolled as in the Examine option (described above).
View Graph
The View Graph option allows access to a screen that displays the histogram (Figure 7-8). The resulting histogram is
accompanied by a box plot (described in the Probability Plot Option of the Results menu), and some univariate statistics.
Data File : C: SGeaEftSMJataSExamplr.dat
IMriahln : Cadnium
Loner
Upper
Lin It :
Linit :
«-) Upper Limit
1
Z
3
4
5
6
7
8
9
te
KseT
1.000
2.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
.000
16.700
Freq . Sum
3
4
5
1
5
H
4
5
4
Srrnll. oir
Ucicjhts
3.009
4.009
5.000
1.000
5.000
U.OUO
4.000
5.009
4.009
to Qui
Class Hin. :
Class Uidl.li :
Kcl F. Max
.050
.067
.083
.017
083
.1X1
.667
.083
.067
Q
1
Value
.900
1.700
4.900
4.400
5 800
7.000
7.600
9.900
19.900
000
000
Class Hean
.300
1.425
3.668
4.400
5.509
6.658
7.275
8.688
9. 825
Geo-EAS 1.2.1
7-6
Stall
-------
Stad
Hiitovut
D>*> file •xwpU.dat
1 1 1 1
9-
1 '•'
I
i
•
L
3.
e.
| — |
i—
—
— |
1
8. 4. 8. 12.
Ctdniun (ppn>
-
n
N Totil a
N Miss e
N Uud 50
75th X 10.800
fexinun 16.780
14. 20.
';?,-
Geo-EAS 1.2.1
7-7
March 1991
-------
SECTION 8 SCATTER
8.1 WHAT SCATTER DOES
Scatter produces scatter plots of variable pairs in a Geo-EAS data file. Options allow for log and semi-log plots and for
a regression line to be calculated. Scaling and numeric tickmark labeling for the axes, and titles are computed
automatically.
8.2 DATA LIMITS
Scatter requires that the input data file contain at least three but not more than 48 variables. These should consist of an
X and Y coordinate and a third variable which will be posted. The data file may contain up to 10,000 samples. If the data
file contains more than 10,000 samples, only 10,000 will be used by Scatter.
8.3
THE MENU HIERARCHY
Data
Variables
Execute
8.4 THE MAIN MENU
The Main menu and screen (Figure 8-1) has the options to allow specification of the data file name, the selection of the
variables to be used and other program options. The menu line appears as follows:
Prefix Data Variables Options Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
File Prefix
Data File:
Variables
X Uariahlr
V Variable
A progran fur producing scatter plots
CtSGeoEASSDataS
Exanple.dat
Cadniu* Log : Ofr
Lead Log : Off
Options
Regression : Ves
Equal Scaling : No
1 Data records : 69
1 Hissing data : 0
Execute
Use this option to create the
plot.
Prcf ix Data U«r lab Ics Opt ions HHJJUU-I Qu \t
Generate the plot
Geo-EAS 1.2.1
8-1
Scatter
-------
Data
The Data option is used to enter the name of a Geo-Eas data file.
Variables
The Variables option allows the selection of variables that are to be used as the X and Y coordinate values, and the sample
values to post. The choices available are the variable names as specified in the data file. The screen fields accessed from
this option are:
X Variable A toggle field for selecting the variable name whose values will be used as the X-coordinates.
The default X Variable is the first variable in the data file.
Y Variable A toggle field for selecting the variable name whose values will be used as the Y-coordinates.
The default Y Variable is the second variable in the data file.
Log Two two-valued toggle fields to enable or disable a logarithmic transformation of the X and/
or Y coordinate values. The choices available are "On" (use logarithmic scaling), and "Off.
If the log option is set and the number of missing data (data values less than zero, or the
missing value) is equal to the number of data records, an error message is displayed. The
default value is "Off
Options
The Options option allows selection of linear regression, and a scaling option. The screen fields accessed from this option
are:
Regression A two-valued (Yes/No) toggle field to enable or disable the calculation of a regression line.
The regression line and the coefficients are plotted on the graph. The coefficients are the
slope and intercept of the line represented by the equation Y = Slope * X + Intercept. The
Slope, Intercept and correlation coefficient (R) are displayed to the right of the graph. The
default value for Regression is "Yes".
Equal Scaling A two-valued (Yes/No) toggle field to enable or disable the use of equal scaling on the plot.
If Equal Scaling is selected the true X and Y proportions are maintained on the screen. If this
option is not enabled, the graph will be scaled to fill the screen. The default value is "No"
(disabled).
Execute
The Execute option is used to display the plot on the screen. After the graph has been displayed, type to clear the
screen and return to the Main menu. Figure 8-2 displays an example scatter plot.
4W.
in.
| *«,.
188.
e.
•
Scatter Plot
froit data file exanple.dit
*
i
•'. /^
i^tt??*
Regression Results
H Purs : tit
Slope •. 4.471
Intercept : -J.445
Correl. coeff . : .461
4. 8. 12. 14. 28.
Cadntun
/' S -X,"/ /*' ".
Geo-EAS 1.2.1
8-2
March 1991
-------
SECTION 9 PREVAR
9.1 WHAT PREVAR DOES
Prevar is apreprocessor program for the program Vario. All variogram calculations use the distance and relative direction
between pairs of points in the sampled area. Prevar computes these so that variogram parameters may be changed and
variograms recalculated more quickly in Vario. The output from Prevar is a "pair comparison file" (PCF). The pair
comparison file contains the input data file contents along with distances and relative directions between pairs of sample
points. This information is used by the program Vario to calculate variogram values. Limits may be imposed on the X
and Y coordinate values or on the distance between points in a pair. If no limits are specified, all sample points are used
for calculation. The pair comparison file can become quite large if there are many points in the data file. It is
recommended that some limits on the distance between points be specified.
9.2 DATA LIMITS
Due to the storage requirements of Vario, Prevar must impose limits on the number of sample points in the input file and
on the number of pairs for which distances and directions are computed. The input data file may contain up to 1000
samples and 48 variables. If more than 48 variables exist the data file may not be used. If more than 1000 samples exist
only the first 1000 will be used. If there are N sample points in an input data file and no
inter-pair distances and directions would be computed. A file with several hundred samples would easily generate too
many pairs for Vario. The Limits and Subset options are used to restrict the number of pairs computed. Prevar will
compute a maximum of 16384 pairs.
9.3 THE MENU HIERARCHY
— Prefix
Fites
Variables
limits
Execute
V Quit
9.4 THE MAIN MENU
A preprocessor for progran VARIO
Flic Prefix: C:sGcoEflSsDatas
riles
Ddtd File:
Fair Conparlsnn File:
Variables
X Variable:
V Variable:
Exanple.dat
Exanple.pcf
Easting
Northing
Lin Its
Nlninun MaximiM
X: Z54.460 432.606
v: nu.oea 315. eoe
Distance: .009 368.647
Variables :
Records
Pairs passible:
Fraction: 1.006
Execute
Select this option
pair comparison f 11
and directions for
be computed, sorted
5
60
1770 nax:i63B4
Seed: 2153
tn build the
e. Distances
all pairs Mill
and saved.
Prefix Files Variables Units Subset
Build the pair conparlson file
Quit
Geo-EAS 1.2.1
9-1
Prevar
-------
The Main screen and (Figure 9-1) menu has the options to allow specification of the input data and the pair comparison
file names, the selection of the variables to be used and the limits on sample coordinates and the interpair distances. The
menu line appears as follows:
Prefix Files Variables Limits Subset Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Files
The Files option is used to enter the input data and the pair comparison file names. The screen fields accessed from this
option are:
Data File An alphanumeric field that may be up to 14 characters used for entering the name of a Geo-
EAS data file.
Pair Comparison
File An alphanumeric field that may be up to 14 characters used to specify the name of the pair
comparison file. This file will contain the contents of the input data file, and the information
for each pair of samples, the distance between the two sample points and their relative
direction. The default Pair Comparison File is the name of the data file with a .pcf extension.
For example if the Data File is "Example.dat", the default Pair Comparison File would be
"Example.pcf'. If the file already exists a Yes/No prompt provides alternatives to continue
or quit from the option.
Variable
The Variable option allows the selection of the variables that are to be used for the X and Y coordinate values. Thechoices
are determined by the variable names in the input data file. The screen fields accessed from this option are:
X Variable A toggle field used for selecting the variable name whose values will be used as the X
coordinates. The default X variable is the first variable in the data file.
Y Variable A toggle field used for selecting the variable name whose values will be used as the Y
coordinates. The default Y variable is the second variable in the data file.
Limits
The Limits option is used to restrict the area and interpair distance for pairs retained in the pair comparison file. The screen
field accessed from this option are:
Minimum Three numeric fields for entering the minimum X and Y coordinate values and the minimum
distance between pairs. The default values displayed are determined from the coordinate
variables in the data file.
Maximum Three numeric fields for entering the maximum X and Y coordinate values and the maximum
distance between pairs. The default values displayed are determined from the coordinate
variables in the data file.
Subset
The subset option is used to permit sub-sample variograms to be computed from large data sets. The data limit remains
at 1000 records. The screen fields accessed from this option are:
Fraction A numeric field for specifying the cutoff value. Acceptable values range from 0 to 1. If the
value entered is less than 1, a uniform random number between 0 and 1 is generated for each
pair, and the pair is retained only if the random number is less than the value entered. The
default is 1.
Seed A numeric field used for entering the seed to initialize the random number generator. The
default random seed is computed from the system clock.
Geo-EAS 1.2.1 9-2 March 1991
-------
If a Geo-EAS data file has 600 observations, for example, the number of possible pairs is 179,700. Specifying a fraction
of 0.089 will result in a random subset of approximately 16,000 of these pairs in the ".Pcf' file, which may be analyzed
with VARIO. If the subset optin is used, several subsets should be evaluated to ensure that they are giving consistent
results. The user must choose whether to use the limit or the subset option, or both.
Execute
The Execute option is used to initiate computation of pair comparison data and the creation of the pair comparison file.
Distances and pair directions for all pairs in the data file are computed (subject to the limits criteria), sorted by distance,
and saved in the pair comparison file. If the limit of 16384 pairs is reached, a Yes/No prompt will allow an opportunity
to quit or proceed. If this occurs (and you choose to proceed) 16384 pairs will be written to the file, but it probable that
other important contributing pairs will not be included. The better approach would be to uit and to select an interpair
distance limit or coordinate limits to restrict the number of pairs computed.
Geo-EAS 1.2.1 9-3 Prevar
-------
SECTION 10 VARIO
10.1 WHAT VARIO DOES
Vario is a two-dimensional variogram analysis and modeling program. Vario uses a pair comparison file (PCF) produced
by Prevar to calculate variogram values and other statistics for a specified set of pair distance intervals (lags). Tolerances
may be specified for pair direction and lag distance intervals. Plots of variogram values vs. distance may be displayed.
Several graphs of the individual lag results may also be viewed, such as lag-histograms, box plots, postplots and lag-
scatter plots. Variograms may be fitted with a model of up to 4 nested (additive) variogram structures. Lag results for
individual lags may be saved in a Geo-EAS data file for analysis.
10.2 DATA LIMITS
Vario requires that the pair comparison file contains no more than 48 variables, 1000 samples, and 16384 pairs. If there
are more than 48 variables the data file may not be used. If there are more than 1000 samples only the first 1000 will
be used. Up to 24 lag intervals may be defined. As many as 2000 pairs may be used for an individual lag. If more than
2000 pairs exist per lag, only the first 2000 are used.
10.3 THE MENU HIERARCHY
Vario
I Data
| Limits
I
Direction
Kew Lags
Change Lags
Post Plot
Quit
\ Quit
.;Piot. ••/- •;
iBoxPJot..;,
''Lag Results:
.Model •—
\ Quit
— Histogram
j Scatter Plot
Examine
I Write
\ vQuit
— Model'
I PJot
| Options «•>•"
i
±
V Quit
* titles • • •
Tic Spacing
Limits
Geo-EAS 1.2.1
10-1
March 1991
-------
10.4 THE MAIN MENU
• vwmmmimtmmn- >
ft progran for confuting uariograns
File Prefix :C:SGeoEflSSDaUS
File
Pair Comparison File: Exanple.pcf
Uarlable
Variable: Cadniun
Log Option: Off
Units
nininun: .800
Haxlnun: 16.700
Uars 5 « Kept
Data 68 It Obs<=0
Pairs 1770 It Hissing
Uariogran Options
Use this option to displa
Uariogrnn Options Screen
Uariogron options nay be
and OK iMriogran nay be
: 66
: Z
: 8
y the
and Menu.
selected
computed .
Prefix Data Variable Limits
Specify uarlogran options/ compute
Quit
r, /, 'A, y,
s ;" O %•• ' ' •"
The Main screen and menu (shown in Figure 10-1) has options to allow specification of the pair comparison file, the
selection of the variable to be used with associated options, and the variable limits. The menu line appears as follows:
Prefix Data Variable Limits Options/Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Data
The Data option is used to enter the pair comparison file name. The pair comparison file contains distances, directions
and pair pointers for pairs of (2D) sample points in a Geo-EAS data file. This file is produced by the program Prevar
and is a binary (non-readable) file, to conserve disk space.
Variable
The Variable option allows for the selection of the variable that is to be used to compute the variogram. The choices
available are the variable names as stored in the pair comparison file. When the variables are selected the input data are
read from the data file and defaults are computed for sample value limits and lag spacing. If and error occurs while reading
the file an error message is displayed. The screen fields accessed from this option are:
Variable A toggle field for selecting the variable whose values are used as the sample values. The
default Variable is the third variable in the pair comparison file.
Log Option A two valued toggle field to enable or disable a logarithmic transformation of the samples.
The choices available are "On" (use logarithmic scaling), and "Off. The default is "Off.
Limits
The Limits option allows you to enter the values that specify the limits for the sample values. The screen fields accessed
from this option are:
Minimum A numeric field for entering the minimum variable value to use in computation. The default
value is the minimum value of the variable selected.
Maximum A numeric field for entering the maximum variable value to use in computation. The default
value is the maximum value of the variable selected.
Options/Execute
The Options/Execute option provides access to the Options screen and menu (Figure 10-2), described below.
Geo-EAS 1.2.1 10-2 Vario
-------
10.5 THE OPTIONS MENU
**••.
f
u *!»••!
Uariable :CadnJun
nininui. : .806
Direction
Direction : .000
Tolerance : 90.000
Max Bandwidth: MAX
Lag Spacing
ninlnun : .600
naximuii : 302.362
Increment : 15.194
Lag
1
2
3
4
5
6
7
8
9
10
11
12
Pair File
nin. Distance
Max. Distance
Distance Lag
15.194
30.31111
45.582
60.776
75.970
91.164
166.358
121.553
136.747
151.941
167.13Ii
182.329
13
14
IS
16
17
IB
19
20
21
22
23
24
Example. pcf
6.06
362.
Distance
197. 5E3
21Z.717
227.911
243.165
2SB.Z99
273.493
288.687
363.881
leu Lags Change Lags Post Plot Execute Quit
Specify pair orientation (selection) criteria
The Options screen and menu (Figure 10-2) provides a means to specify variogram options, view a post plot of the data
and compute the variogram results. The menu line appears as follows:
Direction New Lags Change Lags Post Plot Execute Quit
Direction
The Direction option allows you to specify the pair orientation (selection) criteria. Figure 10-3 illustrates how these
parameters affect the grouping of pairs within a lag interval. The screen fields accessed from this option are:
Direction A numeric field for entering the pair direction in trigonometric degrees. Acceptable values
range fromOto 180 degrees (excluding 180). The default is zero degrees, which a direction
parallel to the X axis.
Tolerance A numeric field for entering the direction tolerance in trigonometric degrees. Acceptable
value range from zero to 90 degrees inclusive. The default is 90 degrees. The tolerance is
plus or minus. For example, a variogram computed with a direction of 90 degrees and a
tolerance of 10 degrees will include all pairs with an orientation between 80 and 100 degrees.
Max Bandwidth A numeric field for entering the maximum bandwidth. The maximum bandwidth is the
maximum perpendicular distance from the direction centerline to the second point in a pair.
The default value is MAX, meaning that no such constraint is imposed.
Geo-EAS 1.2.1
10-3
March 1991
-------
An illustration of the
function of the Lag
Culloff, Direction,
Tolerance, and
Maximum Bandwidth
parameters.
The pair PI, P7 will be
included in the compu-
lation for Lagl. The
pairs PI, P2 and PI,
P6 will be included in
the computation for
L»g2.
Direction
Angle
X axis direction
New Lags
The New Lags option allows you to choose new pair distance intervals. Pairs are included in a lag if the distance for the
pair is greater than the previous cutoff value and less than the cutoff value for that lag. The screen fields accessed from
this option are:
Minimum A numeric field for entering the minimum inter-pair distance. The first lag will contain pairs
strictly greater than this value.
Maximum A numeric field for entering the maximum inter-pair distance.
Increment A numeric field for entering the increment between lag cutoff values.
The defaults for these fields are calculated as: Minimum = 0.0, Maximum = the maximum interpair distance, and
Increment = Maximum divided by 20.0. These values may not be appropriate for the data configuration. Once these
parameters are specified, the lag cutoff distances are displayed in columns on the Options screen.
Change Lags
The Change Lags option allows you to change the lag cutoff distances on the Options screen. This provides a means of
specifying unequal lag intervals. The screen fields accessed from this option are a group of numeric fields for entering
new lag cutoff values. After these have been entered the program will sort the values by increasing distance and re-display
them, if necessary.
Post Plot
The Post Plot option allows you to view a post plot of the dam. This plot shows the actual locations of the sample points.
Each point is labeled with a "+" character. The X and Y axes are automatically scaled and labeled. This graph is useful
in determining the lag cutoff distances for the New Lags option. Figure 10-4 displays an example post plot for
Example.dat.
Geo-EAS 1.2.1
10-4
Vario
-------
f ff fs f f fffjy ff f /
„' ' «»' '',"/»
Plot of sanplg locations
328.
288.
249.
£ 288.
Iti.
128.
320. 400, 480.
Caiting
^"*'
Execute
When the Execute option is selected the program displays the Results screen and computes the lag results before
providing access to the Results screen and menu (Figure 10-5). This menu is described below.
10.6 THE RESULTS MENU
Variable:
Mininun
Maxinun
Pairs
1 17
2 65
3 97
4 111
5 141
6 194
7 193
8 165
9 147
18 115
11 146
12
Caahiui
.BOB
16.700
Avg Distance
11.996
23.837
38.114
52.658
67.330
82.717
97.650
111.726
127.411
141.538
157.869
Direction : .008
Estinator : Variogron Tolerance : 90.000
Total Pairs : 1388 BondUidth : n/a
Est inate
7.018
8.838
1 1 . 396
12.996
13.380
15.834
15.842
16. 182
16.460
15.696
18.282
Pairs Avg Distance Est inate
13
14
15
16
17
18
19
20
21
22
23
24
Type 5B! Box Plot 1-00 Results Model Quit
Plot the selected estinotor vs. average distance
The Results screen and menu (Figure 10-5) has options to select the type of estimator to be computed, to view a variogram
and box plots, to recompute detailed results for a specific lag, and to display the Modeling screen and menu. The menu
line appears as follows:
Type Plot Box Plot Lag Results Model Quit
Type
The Type option allows for the selection of the type of estimator to display and model. The screen field accessed from
this option is a toggle field. The choices available are: "Variogram", "Relative", "Madogram", and "InvCov (short for
the more descriptinve term "Inverted Covariance". The default is "Variogram". See the glossary for a definition of these
terms.
Geo-EAS 1.2.1
10-5
March 1991
-------
Plot
The Plot option allows you to view a variogram plot of the selected estimator. The distance (h) is plotted along the
horizontal axis, and the variogram isplotted on the vertical axis. The type of estimator and the variable name are displayed
as the graph title. Vertical and horizontal axes scaling and the tick mark spacing are calculated by the program. Displayed
on the right side of the graph are the number of pairs, the lag minimum and maximum, the direction, tolerance and
maximum bandwidth, the sample limits, and the mean and variance of the sample values. An example graph is displayed
in Figure 10-12 near the Plot option in the Modeling screen.
Box Plot
The Box Plot option allows you to view a variogram boxplot, displayed in Figure 10-6. This is a plot which displays
statistical information about each lag. The vertical lines represent the range of values in the lag, with the minimum value
at the bottom and the maximum value at the top. The rectangle superimposed over the vertical range line is the inter-
quartile range. The bottom on this rectangle is the first quartile, and the top is the third quartile. Therefore, 50% of the
data falls within the range represented by the rectangle. The mean is represented by "x" and the median is represented
by the horizontal line through the rectangle. The distance (h) is plotted along the horizontal axis, and the difference
squared is plotted on the vertical axis. The variable name is displayed in the title of the graph. Vertical and horizontal
axes scaling and the tick mark spacing are calculated by the program. Displayed on the right side of the graph is the
number of pairs, the lag minimum and maximum, the direction, tolerance and max bandwidth, the variable minimum
and maximum, and the mean and variance of the data.
Boxp.ot for Cadniun
1
iUpy^
File
Pairs
Direct,
To).
HaxBand
Cadniun
Hininun
Mean
Var
exanple.pcF
1388
BOB
9B.B8B
n/»
7.E85
li.273
Lag Results
When Lag Results option is selected you will be prompted to select a lag number before access is provided to the Lag
Results screen and menu. This is accomplished by using the and keys to move the cursor bar to the desired
lag number and pressing . See the section on the Lag Results menu below for more information.
Model
.The Model option provides access to the Model screen and menu. Sec the section on the Modeling menu below for more
information.
Geo-EAS 1.2.1
10-6
Vario
-------
10.7 THE LAG RESULTS MENU
Lag Nunber
Number of Fairs
Heart :
Variance :
»»:¥•»;«>!
6
191
«!••*•
Hin Distance (GI)
Max Distance (IE)
ftuerage Distance
All data Lag data Fron (pairs)
7.885 8.286 8.286
15.273 11.131 11.131
Spatial correlation estimators
Uariogran
Helatiue Uaria.
Hadogran
InuCou Uario. :
: 15.831
: .231
: 2.219
17. M7
Statistics for
Hinimui
2Gtli x-tlle
Median
Mean
75tli x-tile
Haxinun
75.088
96.000
82.717
To (pairs)
8.286
11.131
difference^
.696
1.690
16.606
31.668
13.560
: 219.640
!IMIIWi)!lu| Scatter Exanine Write (Juil
Generate a Lag-Histogram
The Lag Results screen and menu has options to allow you to view detailed results for a specific lag. The menu line
appears as follows:
Histogram Scatter Examine Write Quit
Histogram
The Histogram option allows you to view a lag-histogram plot. The bars on the histogram represent the number of squared
differences (increments Z(x)-Z(x+h)) in each histogram class. A box plot is appears at the top of the graph to display
the frequency distribution of the entire set of differences. The variable name is displayed in the title of the graph. Vertical
and horizontal axes scaling and the tick mark spacing arc calculated automatically by the program. Displayed on the right
side of the graph is the lag number, the number of pairs, the variogram value, the minimum and maximum distance used
in computing the lag, the direction, tolerance and maximum bandwidth, and the sample value limits. An example lag-
histogram plot is displayed in Figure 10-8.
Scatter
The Scatter option allows you to view a lag-scattergram. This is a plot of pairs of sample values. Every pair of sample
values is represented as a point in the scatter plot, where the X coordinate is the value of the first point in the pair and
the Y coordinate is the value of the second point in the pair. Points arc plotted for all pairs in the lag, subject to the limits
criteria (direction, tolerance, bandwidth, sample value limits and intcrpair distance) which have been specified.
Displayed on the right side of the graph is the lag number, the number of pairs, the variogram value, the minimum and
maximum distance, the direction, tolerance, and maximum bandwidth, and thesample valuclimits. Figure 10-9 displays
an example lag-scattergram.
Geo-EAS 1.2.1
10-7
March 1991
-------
120.
IK).
.
! *••
i
20.
e
—
Lag Histogran Tor Cadniun
TRu ^
SB ue. 240, 32
to <9> keys to scroll to a position on the screen. Press to position the list at the largest squared difference and
to view the smallest. Type to clear the screen and return to the Lag Results menu.
Geo-EAS 1.2.1
10-8
Vario
-------
; 5'^'» -, M
-"V< '^&
¥M& txaiaite
Fair
43:
56:
40:
52:
32:
57:
46:
58:
29:
55:
36:
57:
50:
50:
57:
57:
pr
*
1=1
1st Value
27
29
20
34
6
17
43
29
25
29
20
22
33
32
45
29
t or
4
11
10
11
1
16
15
11
11
11
16
14
14
16
16
409
000
400
600
209
TOO
000
600
900
BOO
600
700
900
900
TOO
700
1 to srrn H '
MMMMI
!'«:«:••:•>•
2nd Ualue
14
1
11
6
4
11
4
1
1
1
509
909
009
200
609
109
409
900
609
909
009
000
700
200
600
900
<1> thru <'')* i
mmmmmm
Distance
82
78
78
89
80
78
76
83
88
88
79
73
B'J
BO
B4
76
420
388
954
095
936
359
059
036
522
630
010
'JOG
000
000
S21
340
Direction Dtfference"2
234.382
284.178
223.152
72.746
74.521
207.350
50.870
246.150
83.774
300.964
2B5.066
81.363
90.000
270.000
300.660
264.508
102
102
108
108
108
112
112
114
114
118
.010
.010
.160
.160
.160
.360
.360
.490
.490
.810
134.560
161
174
W7
228
249
.290
.240
.690
.010
.640
Write
The Write option allows you to save the lag results in a Gco-EAS data file. The Variable, From , To Distance,
Direction, Difference and DifferenceA2 will saved in a file. The file name is entered on the message line, when the Write
option is selected. The default file name is "LagResult.dat". If the file already exists, a Yes/No prompt provides an
alternative to quit or proceed. The lag results file may be used wilh other Geo-EAS programs for a more detailed analysis
of the pair information.
10.8 THE VARIOGRAM MODELING MENU
The Variogram Modeling screen and menu has options to allow you to specify the variogram model to display, the graph
options, and to plot the variogram estimates and the specified model. This screen is displayed in Figure 10-11. The menu
line appears as follows:
Model Plot Options Quit
->fif*ff?f«S.. f . > '' s
Screen
Fairs Bug Distance
1
2
3
4
5
6
7
9
ie
11
12
13
14
15
16
17
17
65
97
in
141
194
190
i^cr
4D3
147
115
146
11.996
23.037
38.114
5Z.650
67.330
B2.717
97.650
111 726
127.411
141. 530
157.869
BET
Value
7.01B
o.ton
11.396
12.990
13.380
15.0H4
15 842
tt IB?
ID . LO£.
16.160
15.6%
18.202
m~
Pairs fluij Distance
18
19
26
21
22
23
21
nodcl
Nugget •
Type Sill
Splir.rirnl 11.000
Value
5.000
Range
100.000
Hodel laTBl Options Quit
Flot the variogran and
Model
The Model option allows you to edit or enter the parameters for the variogram model. Up to four nested variogram
structures and a "nugget" component can be included in the model. The screen fields access from this option are:
Geo-EAS 1.2.1
10-9
March 1991
-------
Nugget A numeric field for entering the nugget effect. The value entered must be greater than or equal
toO.
Type Four toggle fields used for selecting the type of variogram structure. The choices available
for each are "Spherical", "Gaussian", "Exponent", "Linear", and " " .If" " is selected
the structure will be ignored.
Sill Four numeric fields for entering the sill for each structure.
Range Four numeric fields for entering the range of influence of the structure. The range of the
variogram structure. The range in a spherical model is the distance at which the model curve
becomes horizontal. In a gaussian and exponential model the range parameter entered is a
"practical range" at which the model attains 95% of its maximum value. In the linear model,
the range and sill are used to define the slope of a linear structure. The practical effect of this
is that the model type can be changed without changing the "apparent range" of the model
curve.
Plot
The Plot option allows you to view a plot of the estimates with specified model superimposed. An example plot is
displayed in Figure 10-12. The distance is plotted along the horizontal axis, and the variogram is plotted against the
vertical axis. The type of estimator and the variable name is displayed as the graph title. Vertical and horizontal axis
scaling and tick mark spacing are calculated by the program. Displayed on the right side of the graph are the total number
of pairs, the minimum and maximum distances, the direction, tolerance and maximum bandwidth, the sample value
limits, and the mean and variance of the sample values. The variance is the population variance as opposed to the sample
variance calculated by the STAT1 program. Press to clear the screen and access the Variogram Modeling menu.
Varioflraii for Cadniui
Pairs
Direct.
lot.
HaxBand
Cadniun
7.885
IS 273
Options
The Options option provides access to the Graph Options screen and menu, displayed in Figure 10-13.
10.9 THE GRAPH OPTIONS MENU
The Graph Options screen and menu (Figure 10-13) has options to select the graph titles and labels, the spacing of the
tick marks, and the graph limits for the graph produced with the Plot option of the Variogram Modeling menu. The menu
line appears as follows:
Titles Tic Spacing Limits Quit
Geo-EAS 1.2.1
10-10
Vario
-------
,
Options Screen
Titles
Nain Title : Uariogran for Cadniun
Subtitle :
X Label : Distance
1 Label : Uariogran
Tickmark Spacing
X Ticknark Spacing : 10.608
1 TlcXnark Spacing : 4.600
Limits
X fix is rtininun : .000
X Axis floxinun ; 160.006
V fix is nininun : .006
V Axis Haxinun : ZZ.006
lilBn Titles Tic Spacing Limits Quit
Plot the graph and nodel curve
Titles
The Titles option allows you to enter the title and labels for the graph. The screen fields accessed from this option arc:
Title
Subtitle
X Label
Y Label
An alphanumeric field which may contain up to 60 characters each, for the title on the graph.
The default title contains the type of estimator and the variable name.
An alphanumeric field which may contain up to 60 characters for the graph subtitle.
An alphanumeric field which may contain up to 60 characters for the X axis label. The
default label is "Distance".
An alphanumeric field which may contain up to 60 characters for the Y axis label. The
default label is the type of estimator selected.
Tic Spacing
The Tic Spacing option allows the specification of the spacing of tick marks on the X and Y axes. The screen fields
accessed from this option are:
X Tickmark Spacing A numeric field for entering the spacing between the X axis tickmarks.
Y Tickmark Spacing A numeric field for entering the spacing between the Y axis tickmarks.
Limits
The Limit option allows you to specify the limits for the X and Y axes. The screen fields accessed from this option are:
X Axis Minimum
A numeric field for entering the minimum coordinate value to be used on the X axis. The
default value is zero.
X Axis Maximum A numeric field for entering the maximum coordinate value to be used on the X axis. The
default value is the maximum distance calculated by the program.
Y Axis Minimum
Y Axis Maximum
A numeric field for entering the minimum coordinate value to be used on the Y axis. The
default value is zero.
A numeric field for entering the maximum coordinate value to be used on the Y axis. The
default value is the maximum variogram value calculated by the program.
Geo-EAS 1.2.1
10-11
March 1991
-------
SECTION 11 XVALID
11.1 WHAT XVALID DOES
The name Xvalid stands for "cross-validation". Cross- validation involves estimating values at each sampled location
in an area by kriging with the neighboring sample values (excluding the value of the point being estimated). The estimates
are compared to the original observations in order to test if the hypothetical variogram model and neighborhood search
parameters will accurately reproduce the spatial variability of the sampled observations. The estimated values,
associated kriging errors, residuals, and other useful statistics are displayed on a summary screen. Scatter plots and
histograms may be obtained for a quick summary of these results. Results may be stored in a Geo-E AS data file for further
analysis.
11.2 DATA LIMITS
Xvalid requires that the input data file contains at least 3 but no more than 48 variables. Two of these variables must
represent the coordinates of sample locations. No more than 1000 samples may reside in the data file. If more than this
number are encountered, only the first 1000 values will be used for cross-validation.
11.3 THE MENU HIERARCHY
Variables
Options/Execute
Searcft
Model
r Map
Seailer Hot
. Histogram ,
~
11.4 THE MAIN MENU
A progran for cross-validating kriging paraneters
File Prefix: C:SGeoEAS\DataV
File
Data File Nane : Exanple.dat
Variables
X coordinate : Easting
y coordinate : Northing
Variable to krlge : Catalan
Log option : Off
1 Variables : 5
1 Data points : 66
* Hissing data : 6 (Z Obs<=6)
Opt Ions/Execute
Use this option to specify the
XUALID kriging options screen.
This screen "111 be presented only
If & file and variables have been
chosen. Once options have been
selected, kriging My begin.
Prefix Data Variables
XUALID options screen
iiii.iiiimai.ja.ii.il (fclit
* f*Sfw fr-r'ffff"*
f -A$w /f
Geo-EAS 1.2.1
11-1
XValid
-------
The Main screen and menu for Xvalid, shown in Figure 11-1, provides options to specify the file prefix, the input data
file and variables, and to access the Options/Execute menu. The menu line appears as follows:
Prefix Data Variables Options/Execute Quit
Prefix
The Prefix option is used to enter the prefix for the data file name.
Data
The Data option is used to specify the name of the Geo-EAS data file to be used for cross-validation. This file must contain
at least three variables consisting of two coordinates and a sampled value.
Variables
The Variables option is used to select the coordinate and sample value variables. They are selected from toggle fields
which contain the variable names from the specified data file. The data file is accessed when these variables are selected.
If an error occurs while reading the data file an error message will be generated. The screen fields accessed from this
option are:
X Coordinate A toggle field for selecting the variable whose values represent the X coordinates for sample
points. The default X Coordinate is the first variable in the data file.
Y Coordinate A toggle field for selecting the variable whose values will be used as the Y coordinates for
sample points. The default Y Coordinate is the second variable in the file.
Variable to Krige A toggle field for selecting the variable to be estimated. The default is the third variable in
the data file.
Log Option A two-valued (On/Off) toggle field for enabling or disabling the Log Option. If the Log
Option is set to "On", kriging will be performed on the natural log of the sample values. If
it is set to "Off, no log transformation will occur. The default value for the Log Option is
"Off.
Options/Execute
The Options/Execute option provides access to the Options screen and menu. See the section below for more information.
11.5 THE OPTIONS MENU
Data File : C:\eeoEA3MktUNExmple.dat
X Uar Inkle: Easting
Y Uarlable: Northing
Kriging : Cadjiiun
Log option: Off
Kriging Type: Ordinary
Search Ellipse Parameters
R Hajor
K Minor
Angle
Hin Dist
80.060
86.966
.060
.060
Distance type : Euclidean
Nun. sectors : 1
Max pts/sector: 8
Nin pts to use: 1
Eopty sectors : 0
Uariogru Nodel
Type
1 Spherical
Z
3
Nugget:
5.606 Global Nean:
Sill Major Range
11.666 160.000
Minor Range
196.996
Ellipse Angle
Type Search Nodel 2SHD Debug quit
Begin kriging the sanple values
ft.
I',
">,,}
4 •
Sv
Geo-EAS 1.2.1
11-2
March 1991
-------
The Options screen and menu, shown in Figure 11-2, has the options to specify the parameters to be used for kriging,
and to initiate the cross-validation process. The menu line appears as follows:
Type Search Model Execute Debug Quit
Type
The Type field is a toggle field used for selecting the type of kriging used in cross-validation. The choices are "Ordinary",
and "Simple". If "Ordinary" is chosen, ordinary point kriging will be performed. If "Simple" kriging is chosen, simple
kriging is performed and a value must be entered for the Global Mean when the Model option is selected.
Search
The Search option provides a means of controlling the neighborhood search used during kriging. Parameters may be
specified to define an elliptical search area. Constraints may be placed upon the number of sectors and the number of
samples to be retained in each sector of the search area, and the type of distance measure to use when eliminating
neighbors from a search sector. Figure 11-3 depicts the search parameters which define the shape of the search ellipse.
The screen fields accessed from this option are:
R Major
R Minor
Angle
a numeric field for indicating the length of the major radius (half the length of the longest axis)
of the search ellipse.
a numeric field for indicating the length of the minor (shortest) radius of the search ellipse.
This value must be less than or equal to R Major, non-zero, and non-negative. The default
value is the value given for R Major. If R Major is equal to R Minor, the search area will be
a circle.
a numeric field for indicating the orientation of the search ellipse. It is given in trigonometric
degrees in the range from zero up to (but not including) 180, and indicates the angle between
the longest axis of the ellipse (specified by R Major) and the sample coordinate X axis. If R
Minor is equal to R Major, a circle search is used and the Angle parameter is ignored.
Search Ellipse and Variogram Anisotropy
Ellipse Parameters
X Coordinate Axis
Min. Dist.
a numeric field for specifying the minimum distance from the estimated sample location to
the nearest neighbor sample. If a minimum distance of zero (the default) is specified, then
any neighboring sample will be used, subject to the complete set of search constraints.
Distance Type a two valued toggle field for selecting the type of distance measure to use when eliminating
neighbors. The choices available are "Euclidean" (the default), and "Variogram". Neighboring
samples are eliminated from consideration when the Max Pis/Sector (Maximum points per
sector) criterion is exceeded in a given sector. If this should occur, only the "closest"
neighbors are kept. If "Euclidean" distance type is chosen, neighbors are eliminated based
upon the euclidean distance from the point to be estimated ellipse center. If "Variogram"
distance is chosen, the variogram function value (as. specified by the Model parameters) for
the computed distance is used as the criterion for elimination of neighbors.
Geo-EAS 1.2.1
11-3
XValid
-------
Model
Num. Sectors a toggle field for selecting how many sectors in which to divide the search ellipse. The
choices available are "1" (the default), "4", and "8". The combination of the Number of
Sectors, and the Max Points per Sector parameters indicate the maximum number of samples
to be used for kriging. This parameter also serves to indicate the number of groups to use for
classification of neighbors. The search ellipse is divided into the chosen number of equally-
sized sectors. If a sample is found to be within the search ellipse, it is flagged with a sector
number. These sector numbers and sample distances are used for elimination of samples
which exceed the Max Points per Sector criterion.
Max. Pts/Sector a toggle field for selecting the maximum number of points which a sector may contain. The
choices range from "1" to a maximum which depends on the number of sectors chosen. If
one sector is specified, up to 24 neighboring points may be used. If four or eight sectors are
selected, the choices are constrained such that a maximum of 64 neighbors may be retained.
If the number of neighbors in a sector exceeds the specified value, the "farthest" samples (as
determined by Distance Type) are eliminated from consideration.
Min Pts. to Use a toggle field for selecting the minimum number of neighboring samples to use for kriging.
The default value or this parameter is "1". If fewer than the specified number are found
kriging is not performed and a missing value is generated for the estimate and kriging
standard deviation.
Empty Sectors a toggle field for selecting the maximum allowable number of consecutive sectors with no
neighbors. The choices available are determined by the Number of Sectors parameter. If one
sector is chosen, then this field is disabled. If more than the specified number of consecutive
sectors are empty, no value is kriged; missing values are generated in place of an estimate
and kriging standard deviation.
The Model option allows specification of the variogram model to use when kriging. Screen fields are provided for a
nugget effect value and up to four nested variogram structures. Each structure is specified with a structure type, a sill
value, and an ellipse of influence. If simple kriging is chosen an additional field is provided for entering the Global Mean.
Each of the four structures has five associated screen fields. Selecting the Model option will cause a cursor bar to appear
in the upper left corner of the models area. The arrow keys may be used to move the cursor bar to fields in the Model
area. To exit the Model area, move the cursor bar out of the top or off to the left of the area, using , or . If
any errors are made when entering variogram model parameters an error message will be displayed and the cursor bar
will be placed at the problem field. The major and minor ranges, and the angles for the additive variogram structures
defined in this parameter group are similar to the search ellipse ranges and angles. Figure 11-3 illustrates how these
parameters define the shape of the ellipse. The screen fields accessed from this option are:
Nugget
Global Mean
a numeric field for entering the nugget value for the variogram model. Only values greater
than or equal to zero may be entered. The default value is zero.
a numeric field for specifying the global mean for simple kriging. If ordinary kriging is
chosen this field is disabled and cannot be accessed. The default value for the global mean
is zero.
The following five fields are present for each of the four nested variogram structures:
Type
Sill
Major Range
a toggle field for indicating the type of the structure. The toggle field choices for type are "
" (none), "Spherical", "Gaussian", "Exponential", "Linear". The default type for all four
structures is "none". If a structure is entered and the type is subsequently changed to "none"
the structure will be deleted from the variogram model. The order of the variogram structures
on the screen is unimportant; neither do they need to be in a contiguous order on the screen.
a numeric field for entering the sill value for a variogram structure. A non-zero, non-negative
value is required here. In a linear variogram structure the "sill" must be chosen so that the
corresponding "range" parameter value(s) will result in the desired slope(s); the actual model
continues to increase indefinitely with distance.
a numeric value for entering the longest range of influence of the variogram structure. The
Major Range must be non-zero, and non-negative. This may be thought of as similar to the
R Major parameter described in the Search option above. In fact, the variogram ellipse of
influence is defined exactly as the search ellipse: with two ranges (radii) and an angle. Note
that the second ellipse is used to select a reasonable subset of neighbors for efficient kriging
- it has no relationship to the variogram model ellipse(s).
Geo-EAS 1.2.1
11-4
March 1991
-------
Minor Range a numeric field for indicating the length of the minor (shorter) range of the variogram ellipse.
This value must be less than or equal to the Major Range, non-zero, and non-negative. The
default value is the Major Range value. If the two ranges are equal, an isotropic variogram
structure is defined. If they are not equal, the two ranges are used to determine the anisotropy
ratio.
Ellipse Angle a numeric field for indicating the orientation of the ellipse for the variogram structure. It is
given in trigonometric degrees in the range from zero up to (but not including) 180, and
indicates the angle between the longest axis of the ellipse (specified by the Major Range) and
the sample coordinate X axis. If the two ranges are equal (isotropic structure) then the angle
is ignored.
Execute
The Execute option is used to initiate kriging. All parameters must be specified before kriging may begin. Several
"Debug Options" (described below) are enabled or disabled with the , the , and the
keys. These keys are used to toggle the debug displays on or off. If your keyboard has status lights for the keys, it is
easy to determine the state of each key. It is important to disable all three Debug Options prior to using the Execute option,
or intermediate results screens will be generated and kriging will proceed more slowly. If your personal computer is
equipped with the proper graphics hardware, a graphics display is generated (Figure 11-4) when the Execute option is
selected. In this display the original sample locations are represented by symbols. The symbol coding is used to classify
the input data into their respective quartiles. As each point is kriged the estimates and associated results are displayed
at the bottom of the screen and the original symbols are over-plotted by symbols which represent the value of the estimate.
On EGA equipped computer systems, the symbols are also color coded. If your computer system has no graphics
capability or has a Hercules graphics card, no graph is displayed, and the results are displayed at the bottom of the Options
screen. During the kriging process the debug displays (described below) may be activated or de-activated to view
intermediate kriging results. Once all sample values have been kriged, a tone signals that the kriging has been completed.
Pressing at this time will cause the Results screen and menu (described below) to be displayed.
Debug
The Debug option is provided on the menu as a means of identifying the keys used for enabling or disabling the Debug
displays. This option does not actually do anything, but moving the cursor bar to this menu option will display the Debug
display names, and the corresponding < -lock> keys which are used to activate them. These displays provide a means
of looking at intermediate kriging results during the cross-validation process. If the , , or
keys are activated during kriging, the corresponding displays will be generated on the screen. To continue
to die next display, is pressed. To disable the generation of such screens, the corresponding keys should be de-
activated. On an IBM AT- style keyboard, these three keys are accompanied by status lights which indicate that the key
is "on", or "off. Refer to the section on program Krige for a detailed discussion of the debug displays.
How to Cancel Kriging
At any time during the kriging process, kriging may be cancelled by pressing the and keys, the and
keys, or the and keys simultaneously and holding them down until the next point has been
Geo-EAS 1.2.1
11-5
XValid
-------
kriged. If this is done a message is displayed indicating that kriging has been terminated. This is useful when the debug
screens reveal a problem with the search or variogram parameters and you wish to change them and re-start. It is important
to remember that the "terminate kriging" keys will not work when any of the three debug display keys is active.
11.6 THE RESULTS MENU
n
Data File
X Uarlakle
* Uarlable
Kriginj
Type
Minium
ZSth Xtllc
Median
75th xtlle
HaxlMM
H
Bean
Std. tev.
: C:\SeoEftSSData\Bcwiple.dat
: Easting
: North Ins
: Cad* luii
: Ordinary
Variable
.eee
5.386
7.666
19.886
16.766
66
7.885
3.9«
1
t
Estimate
3.332
6.713
7.961
9.626
13.817
66
8. 137
2.661
Data used
Hissing data :
Difference
-6.712
-1.969
-.266
2.253
6.932
M
.252
3.376
Kriging Std
2.691
2. 962
3.176
3.357
4.667
66
3.216
.286
66
8
Zscore
-2.262
-.628
-.669
.629
2.641
66
.658
1.636
iJIIIJIIIlililll Scatter riot Histognm Write Exanlne Quit
(lap of kriging error (differences)
The Results menu and screen, shown in Figure 11 -5, is displayed when kriging has been completed. The Results screen
contains information about the data file, variables, and the type of kriging used. Additionally, descriptive statistics are
provided for the original sample values, the kriged estimates, the kriging standard deviations, the differences (between
estimate and observed), and the zscore. The "zscore" is computed as the ratio of the difference to the kriging standard
deviation. The Results menu appears at the bottom of the screen, and provides options to display several graphs, to
examine the individual results, and to save the results to a Geo-EAS data file. Graph scaling, titles, and labeling are
performed automatically. On a non-graphics computer system the graphs are not generated. The menu line appears as
follows:
Error Map Scatter Plot Histogram Write Examine Quit
Error Map
The Error Map option provides a graph of the kriging error, or "Differences". An example plot is displayed in Figure
11-6. Sample locations are marked with a "+" symbol for over-estimation (Estimate-Observed > 0), and an "x" symbol
for negative differences. The size of the symbol is proportional to the error, so that large positive or negative differences
are easily noticed. Descriptive statistics for the differences are displayed to the right of the graph.
B t » t lit I o I
48
a
49
.232
3.374
-4.712
-J.9W
-.288
2.233
4.732
73th X
HaMlnun
^•*/,"% ' ' / &t!f" ''
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Geo-EAS 1.2.1
11-6
March 1991
-------
Scatter Plot
The Scatter Plot option provides a choice of displaying one of two possible scatter plots. When this option is chosen a
two- valued toggle field containing the choices "Observed vs. Estimate", and "Estimate vs. Error" is displayed on the
message line. It is used to select the type of scatter plot to be displayed. Once this choice has been made the appropriate
graph will be displayed. Box plots are drawn opposite to each coordinate axis to convey information about the frequency
distributions of the observed values and estimates, or estimates and differences. In both types of graph "+" and "x"
symbols are used to indicate positive and negative estimation errors (same as the Error Map option described above).
An example plot is displayed in Figure 11-7.
SoattOT- Plot
Crf>» Validation for Cadniun
r—i
Histogram
istogram option provides a histogram (frequency distribution graph) of the estimation error. An example plot is
i in Figure 11-8. Histogram class intervals are computed automatically by the program. A box plot of the
TheHisi
shown
differences appears at the top of the graph. Descriptive statistics are displayed to the right of the histogram.
m -,;
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23th x -i. ray
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73th X 2.233
ibxiiwi t.m
4. 8.
Dlrr«r«nce: E.timt.-C.dniu"
Geo-EAS 1.2.1
11-7
XValid
-------
Write
The Write option is used to store the result to a Geo-E AS data file. When this option is chosen a prompt for the file name
appears on the message line. If the specified file exists, a Yes/No prompt will provide an option to overwrite, or quit.
If any errors occur while saving the results to the file, appropriate error messages will be displayed on the message line.
If results were successfully saved, a message will be displayed, and pressing any key will re-activate the Results menu.
The file created by this option contains seven variables. The first three are the two sample coordinate variables and the
sample value variable chosen for kriging. The remaining four variables are named "Zstar", "Zsdev", "Zstar-Z", and
"Zscore". They contain, respectively, the estimate, the kriging standard deviation, the estimation error, and the zscore
(estimation error divided by the kriging standard deviation). This file may be used with other Geo-EAS programs for
further analysis.
Examine
The Examine option provides a means of directly examining individual results of kriging on a scrolling display, called
the Examine Results screen. This screen is shown in Figure 11-9. The observed values, estimates, errors, kriging standard
deviations, and zscores are displayed in columns on this screen. These values are ranked in order of estimation error,
so that the largest negative difference is at the top of the list, and the largest positive difference is at the bottom of the
list. The leftmost column contains the sample sequence number in the input data file. The , , ,
, , and keys may be used to position the list on the screen. The numeric keys <1> through <9>
are used to scroll the list in increments of 10% (e.g. pressing <5> would position the middle of the list on the screen).
The key is used to exit the Examine Results screen and return to the Results screen and menu.
• Observation
56
57
1
44
28
18
12
41
36
46
27
52
55
25
58
4
14.966
16.799
11. 506
16.466
12.166
7.266
9.566
16.086
11.666
15.696
14.566
11.666
11.866
11.686
11.686
16.766
Estlmte
8.188
16.217
5.682
5.828
7.765
3.332
5.658
6.396
B.837
12.492
12.249
9. 438
9.793
9.626
9.691
8.791
gpy^ggUgigj
Difference
-6.712
-6.483
-6.418
-1.572
-1.335
-3.B6B
-3.842
-3.616
-2.763
-2.598
-2.251
-Z.162
-2.867
-1.974
-1.989
-1.989
Krlging Std
3.314
2.866
3.498
3.887
3.118
3.469
3.897
3.267
3.875
2.B77
2.337
3.Z23
3.234
2.B98
3.163
3.169
Zscore
-2.626
-2.262
-1.835
-1.176
-1.396
-1.134
-1.241
-1.126
-.899
-.963
-.766
-.671
-.626
-.683
-.683
-.614
Geo-EAS 1.2.1
11-8
March 1991
-------
SECTION 12 KRIGE
12.1 WHAT KRIGE DOES
Krige is an interactive program which performs two- dimensional kriging. A rectangular grid of kriged estimates is
created and stored in a Geo-E AS data file. Contour plots may be generated from these gridded estimates with the program
Conrec. Options are provided to control the type of kriging, the neighborhood search area, the grid spacing and extents,
and the variogram model for each variable kriged. Up to ten variables may be kriged in each program execution. The
program parameters may be stored in a parameter file and retrieved for later use. During the kriging process, debug
displays may be activated or de-activated for the purpose of viewing intermediate kriging results.
12.2 DATA LIMITS
Krige requires that the input data file contains at least three but no more than 48 variables. Two of these variables must
represent the coordinates of sample locations. Up to ten variables may be selected for kriging. No more than 1000
samples may reside in the data file. If more than this number are encountered only the first 1000 values will be used for
kriging.
12 J THE MENU HIERARCHY
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12.4 THE MAIN MENU
A program for kriging a grid of estlnates
rile Prefix: CiSGeoEASsDataS
Read ParAMcter Pile
Input
Parameter File:
Save Parameter File
Output
Parameter File:
Prefix
Use this option to enter a prefix
•hich is used to build file Tunes
used by the progrw.
Read Paraneten Optlore/Execute Saue Parameters Quit
Enter the Prefix for files
Geo-EAS 1.2.1
12-1
Krige
-------
The Main screen and menu for Krige, shown in Figure 12-1, provides options to specify the file prefix, to read or save
program parameter values in a parameter file, and to access the Krige Options menu, where program parameter values
are specified and kriging is initiated. The menu line appears as follows:
Prefix Read Parameters Options/Execute Save Parameters Quit
Prefix
The Prefix option is used to enter the prefix for the data file name.
Read Parameters
The Read Parameters option provides a means of loading program parameter values from a parameter file. When this
option is selected a prompt is issued for the Input Parameter File name. A default name is constructed from the most
recently used Geo-EAS data file name using the file extension "kpf' (krige parameter file). Once the name has been
specified the parameter file is accessed and the parameters are retrieved from the file. The data file is also accessed at
this time so that the coordinate variable values may be loaded by the program. If an error occurs while trying to access
or read the parameter or data file, a message will be displayed indicating the problem, and any key may be pressed to
return to the Main menu. If parameters and data are successfully loaded a message will be displayed, and pressing any
key will cause the Krige Options screen and menu to be displayed.
Options/Execute
The Options/Execute option provides access to the Krige Options screen and menu. See the section below for more
information.
Save Parameters
The Save Parameters options provides a means of storing program parameter values in a parameter file for later use.
When this option is selected a prompt is issued for the Output Parameter File name. A default name is constructed with
a "kpf file extension as described above for the Read Parameters option. If the named file already resides on disk, a Yes/
No prompt provides a means of overwriting the old file or exiting the option. If an error occurs while trying to create
or write to the Output Parameter File a message will be displayed, and pressing any key causes re-activation of the Main
menu. If the parameters are successfully stored in the file, a message is displayed and a keystroke re-activates the Main
menu.
12.5 THE OPTIONS MENU
''^vrV^Jfe- s
/*
Title: Exaiiple.grd - krlged estimates of data
Data
Data File : Exanple.dat
Output File : Exanple.grd
Polygon
Polygon File:
Sample Select: Ito
Type
Type of Kriging : Ordinary
Point or Block : Block 2x2
Grid Parameters
Uarlable East
Origin
Spacing
Number
Search Parameters
from Exanple.dat
X Y
ng Northing
266.688 128.888
26.668 28.866
13 11
Major Radius : 53.466 t Sectors :
Minor Radius : 59.466 Max in Sector:
Ellipse Angle: .666 Hin. to use :
Distance Type: Euclidean Empty Sectors:
1
B
1
8
DaU Polygon Type GrU Search IJWIMB.IHil.ingB Title Execute
This option invokes the Variables and Uarlogran node Is screen
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The Options screen and menu (Figure 12-2) has the options to specify the parameters to be used for kriging, and to initiate
the kriging process. The menu line appears as follows:
Data Polygon Type Grid Search Variables/Models Title Execute Quit
Geo-EAS 1.2.1
12-2
March 1991
-------
Data
The Data option is used to specify the name of the Geo-E AS data file whose values will be used for kriging, and the name
of the Geo-EAS output file of gridded estimates. The screen fields accessed through the Data option are:
Data File A 14 character alphanumeric field in which the name of the input data file is entered. The
most recently used Geo-EAS data file name is the default. Once the name is given the
program reads the variable names from the file into several toggle fields used for selecting
the coordinate variables and the variables to krige. If the data file cannot be located or an error
occurs while accessing the file an error message is generated. If the variable names are loaded
successfully the Krige Options menu will be re- activated.
Output File A 14 character alpha-numeric field for entering the name of the output file of gridded
estimates. A default name is constructed which consists of the input data file name with a
".grd" extension (signifying gridded data). If the specified file already resides on disk, a Yes/
No prompt provides the alternative of overwriting the file or exiting the option.
Polygon
The Polygon option is used to specify the name of a file containing polygonal boundaries which limit the area in which
estimates are produced and an option to allow the polygon files to operate on samples as well as blocks. The polygon
file should contain one or more lists of polygon vertices which form closed polygons.
For each block (or point) in the grid, a "FLAG" is kept which indicates if the block estimate is to be excluded from
computation. When no polygon files is specified, KRIGE sets all the flags to INCLUDE. If a polygon file is specified,
all flags are initially reset to EXCLUDE, and then modified sequentially by the coded polygons in the file. The codes
result in the following operations:
IF Code = 0 flags are set to INCLUDE blocks INSIDE the current polygon. Blocks outside remain
unchanged.
IF Code = 1 flags are set to EXCLUDE blocks INSIDE the current polygon. Blocks outside remain
unchanged.
IF Code = 2 the flag settings are REVERSED for blocks INSIDE the current polygon. Blocks outside
remain unchanged.
IF Code = 3 the flag settings are REVERSED for blocks OUTSIDE the current polygon. Blocks inside
remain unchanged.
The new Sample Select option can be set to YES or NO, resulting in operation as follows:
IF Sample Select = NO
(the default) the polygon option operates only on points or blocks to be kriged - all samples in the data file
are used for Kriging.
IF Sample Select = YES the polygon option operates on both the points or blocks to be Kriged AND on the samples.
Only samples within areas flagged INCLUDE are used for kriging.
The polygon file is read when the Execute option is used to initiate kriging. If an error occurs while reading the Polygon
file, a message will be generated, the file will be ignored and an attempt to krige all grid cells will be made. See the
appendices for a detailed description of the polygon file format.
Type
The Type option is used to select the type of kriging to use and whether to krige point or block estimates. The screen
fields accessed from this option are:
Type of Kriging A toggle field containing the choices "Ordinary", and "Simple" which is used to specify the
type of kriging to perform. If "Ordinary" is chosen, ordinary kriging will be performed. If
"Simple" kriging is chosen, simple kriging is performed and a value must be specified for
the Global Mean when entering the variogram model parameters on the Variables/Models
screen.
Point or Block A toggle field containing the choices "Point", "Block 2x2", "Block 3x3", and "Block 4x4",
which is used to indicate point or block kriging. If one of the "BlockNxN" choices is selected,
Geo-EAS 1.2,1 12-3 Krige
-------
block estimates will be produced. The "N" refers to the number of discretization points used
to approximate the area of the block. Large "N" values give somewhat better approximations
of the blocks at the expense of increased computing time. The choice of point or block also
determines the meaning of the Grid Origin parameters. If block kriging is chosen these
parameters refer to the center of the lower left-hand block in the grid.
Grid
The Grid option is used to specify the variables to use as coordinate values, the origin of the grid, the size of grid cells,
and the number of cells in the X and Y directions. These are specified with four screen fields for each of the two directions.
The screen fields for the X and Y directions are:
Variable Two toggle fields containing the variables names from the specified input data file which are
used to specify the variables to be used as the sample coordinate values when kriging. The
default values for the X and Y variables are the first and second variables in the data file. Once
the variables have been chosen the coordinate values are retrieved from the data file. If an
error occurs during the retrieval of data, a message is displayed, and pressing any key will
re-activate the Krige Options menu, but it is assumed that the file is corrupted and cannot be
used. A new data file name must be specified. If no grid parameter values have been
previously specified, default values for the Origin, Cell Size, andNumber of Cells parameters
are computed.
Origin Two numeric fields used for entering the X and Y coordinate values for the origin of the
kriging grid. If block kriging (the default) were selected the origin is taken as the center of
the lower left-hand grid block.
Cell Size Two numeric fields for specifying the grid cell size. For point kriging these values will
indicate the distance between points in the grid. For block kriging these parameters will
indicate the size of the blocks to be kriged (the distance between block centers in each
direction). Both values must be non-zero, and non-negative.
# Cells Two numeric fields for selecting the number of points or blocks to be produced in each of the
two directions. These values must be non-zero, non-negative, and may not exceed 100.
Search
The Search option provides a means of controlling the neighborhood search used during kriging. Parameters may be
specified to define an elliptical search area. Constraints may be placed upon the number of sectors and the number of
samples to be retained in each sector of the search area, and the type of distance measure to use when eliminating
neighbors from a search sector. The screen fields accessed from this option are:
R Major A numeric field for indicating the length of the major radius (half the length of the longest
axis) of the search ellipse.
R Minor A numeric field for indicating the length of the minor (shortest) radius of the search ellipse.
This value must be less than or equal to R Major, non-zero, and non-negative. The default
value is the value given for R Major. If R Major is equal to R Minor, the search area will be
a circle.
Angle A numeric field for indicating the orientation of the search ellipse. It is given in trigonometric
degrees in the range from zero up to (but not including) 180, and indicates the angle between
the longest axis of the ellipse (specified by R Major) and the sample coordinate X axis. If R
Minor is equal to R Major, a circle search is used and the Angle parameter is ignored.
Distance Type A two valued toggle field for selecting the type of distance measure to use when eliminating
neighbors. Thechoicesavai]ableare"Euch'dean"(thedefault),and"Variogram''. Neighboring
samples are eliminated from consideration when the Max Pts/Sector (Maximum points per
sector) criterion is exceeded in a given sector. If this should occur, only the "closest"
neighbors are kept. If the "Euclidean" distance type is chosen, neighbors are eliminated
based upon the euclidean distance from the point to be estimated ellipse center. If
"Variogram" distance is chosen, the variogram function value (as specified by the Model
parameters) for the computed distance is used as the criterion for elimination of neighbors.
Num. Sectors A toggle field for selecting how many sectors in which to divide the search ellipse. The
choices available are "1" (the default), "4", and "8". The combination of the Number of
Sectors, and the Max Points per Sector parameters indicate the maximum number of samples
to be used for kriging. This parameter also serves to indicate the number of groups to use for
Geo-EAS 1.2.1 12-4 March 1991
-------
classification of neighbors. The search ellipse is divided into the chosen number of equally-
sized sectors. If a sample is found to be within the search ellipse, its' sector number is stored.
These sector numbers and sample distances are used for elimination of samples which exceed
the Max Pts/Sector value.
Max. Pts/Sector A toggle field for selecting the maximum number of points which a sector may contain. The
choices range from "1" to a maximum which depends on the number of sectors chosen. If
one sector is specified, up to 24 points neighbors may be used. If four or eight sectors are
selected, the choices are constrained such that a maximum of 64 neighbors may be retained.
If the number of neighbors in a sector exceeds the specified value, the "farthest" samples (as
determined by Distance Type) are eliminated from consideration.
Min Pts. to Use A toggle field for selecting the minimum number of neighboring samples to use for kriging.
The default value or this parameter is " 1". If fewer than the specified number of samples are
found then kriging is not performed and a missing value is generated for the estimate and
kriging standard deviation.
Empty Sectors A toggle field for selecting the maximum number of consecutive sectors with no neighbors.
The choices available are determined by the Number of Sectors parameter. If one sector is
chosen, then this input is ignored. If more than the specified number of consecutive sectors
are empty, no value is kriged and missing values are generated in place of an estimate and
kriging standard deviation.
Variables/Models
The Variables/Models option is used to access the Variables/ Models screen and menu. This screen and menu are used
for selecting the variables to krige and the variogram model to use for each variable. Up to ten variables may be selected
for kriging. At least one must be specified prior to selection of the Execute option. The Variables/Models screen and
menu is discussed below.
Title
The Tide option is used to indicate the descriptive tide to store in the output file of gridded estimates. It provides access
to a 60 character alphanumeric field for storing the title. A default title is constructed from the data file name and the
output file name. Any valid alphanumeric character suing may be entered.
Execute
The Execute option is used to initiate kriging. All parameters must be specified before kriging may begin. Several
"Debug Options" (described below) are enabled or disabled with the , the , and the
keys. These keys are used to toggle the debug displays on or off. It is important to disable all three Debug Options prior
to using the Execute option, or intermediate results screens will be generated and kriging will proceed more slowly.
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Krige
-------
If your personal computer is equipped with the proper graphics hardware, a graphics display (shown in Figure 12-3) is
generated when the Execute option is selected. In this display the original sample locations are represented by the "x"
symbol. As each point is kriged, the estimates and associated results are displayed at the bottom of the screen (except
in Hercules- equipped systems) and the point or block estimates are plotted with a symbol which indicates the quartile
of the estimate. On EG A equipped computer systems, these symbols and the sample values are also color coded. Alegend
is displayed at the right of the screen showing the symbols and corresponding quartile cutoff values. If your computer
system has no graphics capability, no graph is displayed, and the results are displayed at the bottom of the Krige Options
screen.
During the kriging process the debug displays (described below) may be activated or de-activated to view intermediate
kriging results. Once all grid cells have been kriged, a tone signals that the kriging has been completed. Pressing
will cause the Krige Options screen and menu to be displayed and a message will be generated to indicate that the results
were successfully written to the output file. If an error occurs while attempting to write to the file, kriging will be halted
and an error message will be displayed.
How to Cancel Kriging
At any time during the kriging process, kriging may be canceled by pressing the and keys, the and
keys, or the and keys simultaneously and holding them down until the next point or block
has been kriged. If this is done a message is displayed indicating that kriging has been terminated. This is useful when
the debug screens reveal a problem with the search or variogram parameters and you wish to change them and re-start.
Note that in this situation the output file will not contain a completed grid of estimates and probably cannot be used by
the program Conrec. It is important to remember that the "terminate kriging" keys will not work when any of the three
debug display keys is active.
12.6 THE VARIABLES/MODELS MENU
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Krige
1 Catelw g
2
3
4
6
7
8
9
16
Variable : Cainlm Global Mean :
Uariogran Node! Parameters
Nugget : 4. 566
1 Type Sill Value Major Range Hi nor Range Angle
1 Exponent. 13.S66 366.666 166.686 .66
2
3
4
THIPE1BBIHH Edit Delete Quit
Add a nM variable and nodel to the Xrlging Lilt
The Variables/Models screen and menu (Figure 12-4) is provided for selection of the variables to krige and to specify
the variogram model for each of the selected variables. The Variables/Models screen is divided into three areas. The
area on the left of the screen is used to display the list of variables selected for kriging, called the Kriging List. This list
is used as a menu from which to select a variable when deleting or editing a variable/model specification. On the right,
the top area is for selecting new variables to add to the Kriging List and the bottom area is for entering variogram model
parameters. The Variables/Models menu provides options to add or delete a variable and model to the Kriging List, and
to edit a set of variogram model parameters. The menu line appears as follows:
New Variable Edit Delete Quit
New Variable
The New Variable option is used to select a variable to add to the Kriging List A toggle field is displayed in the top portion
of the screen which contains the variable names from the input file. The default value for this field is the third variable
name in the file. Once this selection is made the variable name is added to the Kriging List and the variogram model
parameters (described below) must be entered.
Geo-EAS 1.2.1
12-6
March 1991
-------
*** Note *** it is possible to krige the same variable more than once; the output file will then contain duplicate
variable names.
Edit
The Edit option allows you to edit the specified variogram model for the specified variable. When this option is selected
the Kriging List menu is activated. A cursor may be moved to the appropriate member of the list with the or
keys and selected for editing with . Once the variable has been specified the parameters will be loaded onto the
screen and the Variogram Model Parameters area will be activated. In this screen area fields are provided for a nugget
effect value and up to 4 additive variogram structures. Each structure is specified with a structure type, a sill value, and
an ellipse of influence. If simple kriging is chosen an additional field is provided for entering the Global Mean. Each
of the four structures has five associated screen fields. Selecting the Model option will cause a cursor bar to appear in
the upper left corner of the models area. The arrow keys may be used to mo ve the cursor bar to fields in the Model area.
To exit the Model area, move the cursor bar out of the top or off to the left of the area, using the , or keys.
Ifan>
will!
f any errors are made when entering variogram model parameters an error message will be displayed and the cursor bar
/ill be placed at the problem field. The screen fields accessed from this option are:
Nugget A numeric field for entering the nugget value for the variogram model. Only values greater
than or equal to zero may be entered The default value is zero.
Global Mean A numeric field for specifying the global mean for simple kriging. If ordinary kriging is
chosen this field is disabled and cannot be accessed. The default value for the global mean
is zero.
The following five fields are present for each of the four additive variogram structures:
Type
Sill
Major Range
Minor Range
Ellipse Angle
A toggle field for indicating the type of the structure. The toggle field choices for type are
" (none), "Spherical", "Gaussian", "Exponential", "Linear". The default type for all
four structures is "none". If a structure is entered and the type is subsequently changed to
"none" the structure will be deleted from the variogram model. The order of the variogram
structures on the screen is unimportant; neither do they need to be in a contiguous order on
the screen.
A numeric field for entering the sill value for a variogram structure. A non-zero, non-negative
value is required here. If a linear variogram type is selected the sill value is used together
with the variogram ellipse ranges to determine a slope for a given direction. In a linear
variogram structure the sill must be chosen so that the corresponding range parameter values
will result in the desired slope.
A numeric value for entering the longest range of influence of the variogram structure. The
Major Range must be non-zero, and non-negative. This may be thought of as similar to the
R Major parameter described in the Search option above. In fact, the variogram ellipse of
influence is defined exactly as the search ellipse: with two ranges (radii) and an angle. Note
however that the two ellipses have fundamentally differentpurposes, although the parameters
which describe them are the same
A n umeric field for indicating the length of the minor (shorter) range of the variogram ellipse.
This value must be non-zero, non-negative, and less than or equal to the Major Range. The
default value is the Major Range value. If the two ranges are equal, an isotropic variogram
structure is defined. If they are not equal, the two ranges are used to determine the ratio of
anisotropy.
A numeric field for indicating the orientation of the ellipse for the variogram structure. It is
given in trigonometric degrees in the range from zero up to (but not including) 180, and
indicates the angle between the longest axis of the ellipse (specified by the Major Range) and
the sample coordinate X axis. If the two ranges are equal (isotropic structure) then the angle
is ignored.
Delete
The Delete option is used to delete a variable and model from the kriging list. When this option is selected, the Kriging
List menu will be activated, and the variable to delete may be selected as described in the Edit option. Once this selection
is made, a Yes/No prompt provides the alternative of canceling the deletion. If is chosen, the variable and model
will be deleted and the Kriging List and screen will be regenerated. This option is disabled when the Kriging List is empty.
Geo-EAS 1.2.1
12-7
Krige
-------
* \ "O " '
,- ' - \-',:"•-.„.;,,,
12.7 THE DEBUG DISPLAYS
The debug displays are provided as a means of viewing intermediate kriging results during the kriging process. Since
such displays slow the kriging process, the displays may be activated, or de-activated at any time during kriging. If the
, , or keys are activated during kriging, the corresponding displays will be
generated on the screen. To continue to the next display, the key is pressed. To disable the generation of these
displays, the corresponding keys should be de-activated. On an IBM AT-style keyboard, these three keys are
accompanied by status lights which indicate that the key is "on", or "off. The following is an explanation of each display,
and the key which activates it
V X- . V
S^sfemot Equations
Debug results for variable :C«dnluN
Faint krigcd is :( 366.006, 300.000)
2(1) ACI.J):
18.294
8.677
5.9M
5.866
5.482
3.038
6.713
1.000
IS. 000
6.561
9.328
7.S10
7. 135
3.923
7.383
1.000
6.561
18.000
8.220
3. TOT
3.513
1.918
4.755
1.000
9
8
18
5
5
2
5
1
.329
.220
.000
.312
.489
.619
.347
.000
7
3
5
18
9
6
7
1
.540
.709
.312
.000
.635
.977
.409
.000
7.135
3.513
5.489
9.63S
18.000
6.611
5.508
1.000
3.923
1.918
2.819
6.977
6.611
18.000
4.297
1.000
7
4
5
7
5
4
18
1
.383
.755
.347
.409
.506
.297
.000
000
i.oee
i see
i.ooe
1.900
i.oee
1,000
i.eoe
.960
This activates the Search Area display, shown in Figure 12-5. For each estimate, the search
ellipse is displayed along with all sample locations in the sampled area. The neighbors which
were chosen for the estimate are marked. The coordinates of the estimated point (center of
the search ellipse) is displayed at the top of the screen. If more than one sector was chosen,
the sector boundaries will be plotted. This display may be used to check if the search ellipse
is of the proper size and orientation, and that the desired number of samples are used as
neighbors. On a non-graphics system this display is a text display showing the list of
neighbors, the sample locations, and the sector number for each neighbor.
Geo-EAS 1.2.1
12-8
March 1991
-------
Debug results for variable :C«4iiluN
Point krlged Is
X(i) K(l)
:( 369.869. 189.806)
V(l) H stance y(i)
12(1)
'
". f f ;
'?'•*-,' 4
' 'ff^fff '
.',; •«,",*f,X
\? ffff f %
\f ' ''"'''
?
1
i
•j
s'
•{ ; wi
'--• ->'/&
'f, " 1
- ';;,2
fe'?, '' 1
*"; ' J
•v 1
379.
366.
379.
359.
334.
334.
346.
366.
Neighbors:
EstlMte:
•k:
r«k:
188.
195.
165.
203.
194.
163.
216.
216.
6:18
6.88
6.78
6.38
11.6
8.79
18.8
18.1
9.68
15
17
24
29
31
33
36
.9
.8
.9
.9
.4
.3
.8
8 Z Ucighti:
7.58
1.62
2.61
%
CW
UIB21
F
.384
.142
.165
.324E-61
.123
.124
.1ZBE-61
.171E-91
1.669
11.399
9.299
-.519
11.2
8
8
6
8
7
5
4
.68
.58
.79
.22
.62
.48
.63
X '/
/,
This key activates a display (Figure 12-6) which shows the system of equations used to
produce the estimate. A one-dimensional array of values on the left of the screen shows the
covariances between the estimate location and the neighbors, and the matrix of values in the
remaining portion of the screen shows the covariances between neighboring samples. If the
number of neighbors used in the system of equations is more than eight, each row of the matrix
will "wrap-around" to the next line and produce an undesirable results. This display allows
you to see the actual covariance values used for kriging, for comparison with other programs
or for verification of results.
This key activates the Kriging Weights display, shown in Figure 12-7. This display provides
information about the neighboring samples used for kriging each estimate. This includes the
coordinate values, the sample values, the distances from the estimated point, and the kriging
weights assigned to each neighbor. Also displayed are the kriging estimate, the kriging
standard deviation, and several related statistics, including the sum of the kriging weights,
the kriging variance, and the Lagrange parameter value.
Geo-EAS 1.2.1
12-9
Krige
-------
SECTION 13 POSTPLOT
13.1 WHAT POSTPLOT DOES
Postplot produces a plot of (2D) sample locations and values for a variable in a Geo-EAS data file. Sample locations
may be marked with a symbol, value, or both. The format for the value to be plotted may be specified by setting a scaling
factor and the number of decimal places to be used in the plotted value. Options allow control of axes parameters, and
titles. A file called a "metacode" file is created for redisplay or to produce a hardcopy.
Note: Postplot attempts to produce "true-scale" graphs on the screen, but for some data configurations, an internal NCAR
routine overrides true scaling and produces a somewhat distorted graph.
13.2 DATA LIMITS
Postplot requires that the input data file contain at least 3 but not more than 48 variables. These should consist of an X
and Y coordinate and a third variable which will be posted. The data file may contain up to 1000 samples. If the data
file contains more than 1000 samples, only 1000 will be used by Postplot.
THE MENU HIERARCHY
Postptat*
Prefix
Baia
Variables
Options
Graph Options
Execute
\ Quit
Axis Parameters;
Tick Parameters
Graph Limits
Titles/Labels
\Quit
Eas-GEO 1.2.1
13-1
March 1991
-------
13.4 THE MAIN MENU
The Main screen and menu, shown in Figure 13-1, has the options to allow specification of the data and metacode file
names, the selection of the variables to be used and the options for displaying the posted variable. The menu line appears
as follows:
Prefix Data Variables Options Graph Options Execute Quit
' „„ Screen,,, \
m$ax**$3 / "'
A program tor plotting ZD Maple locations and values
File Prefix : C:\GeoEASsDataS
Data : Exanple.dat
Variables
X coordinate variable : Easting
¥ coordinate variable : Northing
Uariable to post : Cadnlun
Options
Include Ualues No Size : 5
Scale Factor 10* 8
I teclMls 1
Include Su«Vols 4 Size : 4
hetacode File : Itetacode .net
Execute
Use this option to create the
plot. The plot Hill he sawed In
the file specified.
Prefix Data Uariables Options Graph Option
Generate the plot
O.it
ff x" j
MV£*MV X
' ' ?
f
Prefix
The Prefix option is used to enter the prefix for file names.
Data
The Data option is used to enter the name of a Geo-Eas data file.
Variables
The Variables option allows the selection of variables that are to be used as the X and Y coordinate values, and the sample
values to post The choices available are the variable names as specified in the data file. The screen fields accessed from
this option are:
X Coordinate Variable A toggle field for selecting the variable name whose values will be used as the X coordinates.
The default X variable is the first variable in the data file.
Y Coordinate Variable A toggle field for selecting the variable whose values will be used as the Y coordinates. The
default Y variable is the second variable in the data file.
A toggle field for selecting the variable whose values will be posted on the plot. The default
variable to post is the third variable in the data file.
Variable to post
Options
The Options option allows the specification of how the sample locations are to be marked on the graph. The screen fields
accessed from this option are:
Include Values A two-valued (Yes/No) toggle field to enable or disable the labeling of samples with their
numeric values. The choices available are "Yes" - plot values, "No" - do not plot values. The
default value is "No".
Size
Two toggle fields for selecting the character size to use when plotting the values or symbols.
The choices available are "0" to "10", where "0" is the smallest and "10" is the largest
character size. The default size for plotting values is "5", and the default for plotting symbols
Geo-EAS 1.2.1
13-2
PostPlot
-------
Scale Factor
# Decimals
is "4". These choices work well on the screen, however a smaller size might be more suitable
for output to a plotter.
A toggle field for selecting the scaling factor to apply to the values to be plotted. The choices
available range from "10A-4" to "10M". The scaling factor shifts the decimal place left or
rightin theplotted value. For example a scale factor of 10M applied toa value of 7.208 would
result in the value 72080 being plotted. If the Include Values field is set to "No", this choice
is ignored. If the default of "lO'X) "is used the decimal place will not be shifted.
A toggle field for selecting the number of digits to display. The choices available range from
"0" to "3 ". For example, selecting "2" with a value of 72.208 would result in the value 72.21
(round up does occur) being plotted. The default is "1" (one digit to the right of the decimal
place).
Include Symbols A three-valued (4,1, None) toggle field to enable or disable the labeling of samples with their
numeric values. The choices available are "4" - yes plot symbols, "1" - plot using only one
symbol and "None" - do not plot symbols. If the value is "4" (the default) four different
symbols in four different colors will be plotted to represent the values within the quartiles.
A legend is also plotted to show the quartile cutoff values, the symbols, and their corresponding
colors. If the value is " 1" only one symbol, a"+" in one color (yellow) will be used to plot
the values. No legend will be plotted.
Graph Options
The Graph Options option provides access to the Graph Options screen and menu, described below.
Execute
When the Execute option is selected, you will be prompted for a metacode file name. The metacode file is then created
and the graph is displayed. The metacode file name entered may be up to 14 characters. The default value is
"Metacode.met". If the default value is not used and the file specified already exists, a Yes/No prompt for whether or
not to overwrite the file is displayed. This file contains the metacode instructions produced by the program. It will be
saved for future viewing. A hard copy of the graph can be obtained by using the program Hpplot and an HPGL compatible
plotter. After the graph has been displayed, type to clear the screen and return to the Main menu. An example post
plot is shown in Figure 13-2.
Example Fast Pfot
Poatplot of Cadmium -from data fll* •xampl«.dat
3OO
1*1 Quart!)*
2nd Ouartflv:
3rd Ouartil*
4th QuortHw:
Coating <"f««
.000 • +
3.JOO < X
7.OOO < O
10.000 < <#
a.joo
7.6OO
1O.OOO
1 a, TOO
Eas-GEO 1.2.1
13-3
March 1991
-------
13.5 THE GRAPH OPTIONS MENU
Figure 13*3
Postploi Graph
Options Screen
M.r»J!»Wi»M
Axes Parameters
Axis Style: Full
Graph Lin Its
X V
Nin : ZS4.406 118.609
tax • VK.OV3 315.600
liCTil .
tick Parameters
Base
Type
Label
Fract ion
Exponent
Titles/Labels
tain title: Fostplot of Cadniun fro* data file
Subtitles:
X Label: Easting (feet)
V Label: northing (feet)
Auto
Auto
Auto
• Auto
Auto
Exanple.dat
Auto
Auto
Auto
Auto
Auto
Reset Quit
Select style for X and 1 axes
The Graph Options screen and menu, displayed in Figure 13-3, provides control over the "graph background" parameters.
These parameters are used to specify the axis style, the graph limits, titles and axis labels, and the tickmark labeling and
spacing. The menu line appears as follows:
Axis Parameters Tick Parameters Graph Limits Title/Labels Reset Quit
Axis Parameters
The Axis Parameters option allows the selection of the type of axis style for the background of the plot The screen field
accessed from this option is a toggle field. Choices available are "Half (left and bottom axes only), "Full" (left, right,
top, and bottom axes) and "Grid" (the same as "Full", but the major tickmarks extend across to the opposite axis). The
default axis style is "Full".
Tick Parameters
The Tick Parameters option allows specification of the nature of the numeric tickmark labels to be placed along each axis.
This is accomplished with a set of closely inter-related parameters which control the format of the labels. The default
values are initially set to "Auto", and provide adequate labels for most data. With the appropriate selection of parameter
values, however, many useful labels may be constructed, including fractions and superscripted powers often. An excerpt
from the NC AR documentation on tickmark parameters is included in the appendices. Certain incompatible combinations
of parameter choices will result in no labels being plotted or error messages generated by the NCAR Autograph utility.
These errors will cause the program to terminate. To recover, restart and change the parameters. A menu option is
provided to "reset" these parameters to "Auto", so that the default values may be used. The screen fields accessed from
this option are:
Base Two numeric fields used for the computation of major tick marks along the X and Y axes.
The user may accept the default value of "Auto" which allows the system to select the
appropriate value, or enter a value appropriate for the variable selected.
Type Two toggle fields for selecting a formula for computing (using Base, entered above) the
spacing of the tick marks along the X and Y axes. Choices available are:
Auto (System will select appropriate computation)
None (No tick marks on axis)
Base*k
Base * l^k
BaseAk
Note: "k" is an arbitrary integer computed by the program. The default value is "Auto" for both axes.
Geo-EAS 1.2.1
13-4
PostPlot
-------
Label
Fraction
Exponent
Two toggle fields for selecting the format of numeric tickmark labels along the X and Y axes.
Choices available are:
Auto System will select appropriate format
None No tick marks on axis
Scien. Scientific notation
Expon. Exponential notation
No-Exp. Non-exponential notation
Two numeric fields for entering the number of significant digits to display in the numeric axis
labels.
Two numeric fields for entering the value of the exponent in the numeric axis labels.
Table 13-1 shows examples of the types of numeric tick mark labels that can be produced, using combinations of choices
for the Base, Type, Label, Fraction, and Exponent parameters. The labels were produced using the Example.dat data file
with Easting as the X variable and Northing as the Y variable. Remember that certain combinations of parameter values
are incompatible, and will result in unexpected results, or a lack of tickmark labeling. The Reset option may be used to
set parameter values back to their defaults if this occurs.
Base
Auto
Auto
2.
2.
Auto
3.6
Auto
5.
Type
Base*k
Base*10Ak
Base*10Ak
BaseAk
BaseAk
Base*10Ak
BaseAk
BaseAk
Label
Scien.
Expon.
Scien.
No-Exp.
Expon.
No-Exp.
Scien.
Expon.
Fraction
Auto
Auto
1.
-1.
1.
1.
2.
3.
Exponent
Auto
Auto
Auto
Auto
3.
Auto
1.
Auto
Results
2.50 x 102
102
2xl03
64
2X103
30
100.01 x 10°
5.02
Table 13-1 Numeric Tickmark Label Examples
Graph Limits
The Graph Limits option allows you to enter values that specify the coordinate limits for the X and Y axes. Certain
combinations of the Tick Parameters will cause these values to be overridden by the program. The screen fields accessed
from this option are:
Min
Max
Titles/Labels
Two numeric fields for entering the minimum coordinate value to be used on the X and Y
axes. The default values displayed are determined from the variables selected as the X and
Y coordinate values.
Two numeric fields for entering the maximum coordinate value to be used on the X and Y
axes. The default values displayed are determined from the variables selected as the X and
Y coordinate values.
The Titles/Labels option allows you to enter the title and labels for the graph. The Hershy character sets of 33 fonts are
used for plotting alphanumeric labels. Also, certain "special characters" may be embedded in the title or label which
control selection of alternate fonts or other aspects of the plotted text These special characters are not plotted, but are
interpreted as commands by the metacode translator software. The appendices contain information on font selection
codes. The screen fields accessed from this menu option are:
Eas-GEO 1.2.1
13-5
March 1991
-------
Main title An alphanumeric field which may contain up to 60 characters for the main title of the graph.
The default title contains the variable name selected as the post variable and the name of the
data file.
Subtitles Two alphanumeric fields which may contain up to 60 characters each for the subtitles on the
graph. The subtitles appear below the main title.
X Label An alphanumeric field which may contain up to 60 characters for the X axis label. The default
label is composed of the X variable name followed by its units in parentheses.
Y Label An alphanumeric field which may contain up to 60 characters, for the label on the Y axis. The
default label is composed of the Y variable name followed by its units in parentheses.
Reset
The Reset option allows the user to reset the graph options parameters to their default values.
Geo-EAS 1.2.1 13-6 PostPlot
-------
SECTION 14 XYGRAPH
14.1 WHAT XYGRAPH DOES
Xygraph produces line and/or scatter plots for up to six variables in a Geo-EAS data file. Plots of up to six dependent
variables with one independent variable can be obtained. Up to six colors, symbols, and line types may be used to identify
the data. Options allow a regression line to be calculated and axes parameters and graph labeling to be controlled. A
file called a "metacode" file is created for redisplay or to produce a hardcopy.
14.2 DATA LIMITS
Xygraph requires that the input data file contain at least two but not more than 48 variables. The data file may contain
up to 500 samples. If the data file contains more than 500 samples, only 500 will be used by Xygraph.
14.3 THE MENU HIERARCHY
Xygraph Prefix
Options/Execule.
Quit:
Data
Variables
Segression
Legend
Graph Options
Execute
\ Quit
Graph Limits
Reset
\ Quit
Geo-EAS 1.2.1
14-1
March 1991
-------
14.4 THE MAIN MENU
The Main screen and menu (Figure 14-1) has the options to allow specification of the input and output parameter file
names. The menu line appears as follows:
Prefix Read Parameters Options/Execute Save Parameters Quit
Figure 144
An X-y graph plotting progrw
File ?reflx: C:SGeoEASM>ataS
Input Parameter File :
Output Parameter File:
Options
Use this option to select control
parameters, ft Menu of additional
options vill be displayed.
Prefix Head Faraneters HiUliW.-B>l'l.liim.l
Edit, or enter paraneter values
Saue Paraneters Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Read Parameters
The Read Parameters option is used to enter the input parameter file name.
Options/Execute
The Options/Execute option provides access to the Options screen and menu. See the section on Options below for more
information.
Save Parameters
The Save Parameters option is used to enter the name of the output parameter file. If the specified file already exists,
a Yes/No prompt is provided to quit or proceed. The parameter file will contain the current parameter values. It will
be saved for future use as an input parameter file.
Geo-EAS 1.2.1
14-2
XYGraph
-------
14.5 THE OPTIONS MENU
The Options screen and menu (Figure 14-2) has options to allow specification of the data and metacode file names, the
selection of variables to be used, the options for displaying the variable, to compute a regression line, and the position
of a graph legend. The menu line appears as follows:
Data Variables Symbol/Line Regression Legend Graph Options Execute Quit
Figure 14-2
" "
Data File : Exaiple.dat
netacode File : Hetacode.net
Uariables Symbol/Line Type
X Uariable
Arsen ic
V Uariables Synbol Type Line Type
Lead 1 8
z e
3 e
i e
s e
6 e
Color
Black
Blue
Red
Ye llo«
Green
Broun
Regression : Yea
Legend : Hone
Execute
Use this option to create
the graph. The graph Hill
be saved in the file
specified.
Data Uariables Sipibol/Llne Regression Legend Graph Options
Generate the graph
Data
The Data option is used to enter the name of a Geo-EAS data file.
Variables
The Variables option allows the selection of variables that are to be used as the X and Y coordinate values. The choices
available are the variable names as specified in the data file. The screen fields accessed from this option are:
X Variable A toggle field used for selecting the variable name whose values will be used as the
independent variable on the graph. The default X Variable is the first variable in the data file.
Y Variables Six toggle fields used for selecting the variables whose values will be used as the dependent
variables in the graph. The default Y Variable is the second variable in the data file.
Geo-EAS 1.2.1
14-3
March 1991
-------
Symbol/Line
The Symbol/Line option allows the specification symbols and/or lines and color to mark the data on the graph. The
symbols and line types are displayed in Figure 14-3. The screen fields access from this option are:
Figure 14-3
Xygraph Symbols
and Line Types
No symbol
1
2
3
4
5
6
o
x
x/x
No line
1
2
3
4
5
6
Symbol Type
Line Type
Color
Six toggle fields for selecting the type of symbol to plot. There are six choices available ("0"
to "6"). A value of "0" indicates that no symbols are to be plotted. The default Symbol Types
for the six variables are "1" through "6".
Six toggle fields for selecting the type of line to plot for each variable. There are six choices
available ("0" through "6"). A value of "0" indicates that no line is to be plotted. The default
Line Type for all six variables is "0".
Six toggle fields for selecting the color to plot the symbol and/or line pattern. The choices
available are "Black", "Blue", "Red", "Yellow", "Green", "Brown". The default color is
unique for each variable.
Regression
The Regression option provides access to a two-valued (Yes/No) toggle field to enable or disable the calculation of linear
regression. If the value is "Yes" linear regression is only calculated for the first Y variable. The regression line and the
regression coefficients are plotted on the graph. The coefficients are the slope and intercept of the line represented by
the equation Y = Slope * X + Intercept. The correlation coefficient (R) is also plotted. The default is "No".
Legend
The Legend option provides access to a toggle field that is used for selecting the position of the graph legend. The choices
available are "None" (no graph legend), "Bottom" (at the bottom of the graph), and "Right" (at the upper right-hand
comer of the graph). The default position is "None" (no legend).
Graph Options
The Graph Options option provides access to the Graph Options screen and menu, described below.
Execute
When the Execute option is selected you are prompted for a metacode file name. The metacode file is then created and
the graph is displayed. The metacode file name entered may contain up to 14 characters. The default value is
"METACODE.MET", or the name specified in the input parameter file. If the file name is not "METACODE.MET"
and the file specified already exists, a Yes/No prompt provides the option to quit or proceed. The metacode file is saved
on disk for future viewing. An example plot is displayed in Figure 14-4. A hard copy of the graph can be obtained by
using the program Hpplot and an HPGL compatible plotter. After the graph has been displayed, type to clear the
screen and return to the Options menu.
Geo-EAS 1.2.1
14-4
XYGraph
-------
14-4
Cxampl* dot — G«o«tativtrcel Environmental
3OO-I
2OO
Corrvlation Co«fffet«oti .
Arsenic (ppm)
14.6 THE GRAPH OPTIONS MENU
•f f S f flffAffjAQflflfff }dVk/SJUW%
ff VSftf f"f Sw ••* '•tj'tSff
Axes Paruieters
Graph Lin its
Bin :
n« :
Scale:
litles^Ubels
Nain title
Subtitles
X Label
Y Label
Axis Style: Half
X 1
.eoe i.oee
5.610 302.500
Linear Linear
Tick Faraivters
Base :
Type :
Label :
Fraction:
Exponent :
X
Auto
Auto
Auto
Auto
Auto
T
Auto
Auto
Auto
Auto
Auto
: Exaxple.dat - Geostatistical Enuironpental Assessment Sbftua
: Arsenic (pp»)
: Le«4 (pp.)
2IBBQZGSSB Tick farweteri Graph Units Tltle/Labels Reset Quit
Select style for X and T axes
ff Vy tf »!?&&
f 1^1. \ S •S
-*^S!C V -
s''^> 'T;*/
- '3iJ^"?^
^t-/|M'4^"
The Graph Options screen and menu (shown in Figure 14-5) provides control over the "graph background" parameters.
These include parameters which allow control of the axis style, the graph limits, titles and axis labels, and the numeric
tickmark labeling and spacing. The menu line appears as follows:
Axis Parameters Tick Parameters Graph Limits Title/Labels Reset Quit
Axis Parameters
The Axis Parameters option allows the selection of the type of axis style for the plot. The screen field accessed from this
option is a toggle field. The choices available are "Half (left and bottom axes only), "Full" (left, right, top, and bottom
axes) and "Grid" (the same as "Full" but major tick marks are extended across to the opposite axis). The default is "Full".
Tick Parameters
The Tick Parameters option allows specification of the nature of the numeric tickmark labels to be placed along each axis.
This is accomplished with a set of closely inter-related parameters which control the format of the labels. The default
values are initially set to "Auto", and provide adequate labels for most data. With the appropriate selection of parameter
values, however, many useful labels may be constructed, including fractions and superscripted powers often. An excerpt
Geo-EAS 1.2.1
14-5
March 1991
-------
from the NCAR documentation on tick parameters is included in the appendices. Certain incompatible combinations
of parameter choices will result in no labels being plotted or error messages generated by the NCAR Autograph utility.
These errors will cause the program to terminate. To recover, restart and change the parameters. A menu option is
provided to "reset" these parameters to "Auto", so that the default values may be used. Refer to Section 5.9 (Postplot)
for several examples of numeric tickmark labels. The Screen fields accessed from this option are:
Base Two numeric fields for the computation of major tick marks along the X and Y axes. The
user may accept the default value of "Auto" which allows the system to select the appropriate
value, or enter a value appropriate for the variable selected.
Type Two toggle fields for selecting a formula for computing (using Base, entered above) the
spacing of the tick marks along the X and Y axes. The available choices are:
Auto (System will select appropriate computation)
None (No tick marks on axis)
Base* k
Base * K^k
BaseAk
Note: "k" is an arbitrary integer computed by the program. The default value is "Auto" for both axes.
Label Two toggle fields forselectingtheformatofnumericlabeltobeusedatthemajortickmarks
along the X and Y axes. The available choice are:
Auto - System will select appropriate format
None - No tick marks on axis
Scien. - Scientific notation
Expon. - Exponential notation
No-Exp. - Non-exponential notation
Fraction Two numeric fields for entering the number of significant digits to display in the numeric
labels along the X and Y axes.
Exponent Two numeric fields for entering the value of the exponent in the numeric labels along the
X and Y axes.
Graph Limits
The Graph Limits option allows you to enter values that specify the coordinate limits and the type of scaling for the X
and Y axes. Certain combinations of the Tick Parameters will cause these values to be overridden. The screen fields
accessed from this option are:
Min Two numeric fields for entering the minimum coordinate value to be used on the X and Y
axes. The default values displayed are determined from the data file for the variable selected
as the X and Y variables.
Max Two numeric fields for entering the maximum coordinate value to be used on the X and Y
axes. The default values displayed are determined from the data file for the variable selected
as the X and Y variables.
Scale Two toggle fields for selecting the type of scaling to be used on the X and Y axes. The choices
available are "Linear" and "Log" (natural log) scaling. If "Log" scaling is selected and any
data values are negative or zero, an error message is displayed and the Scale field is reset to
"Linear". The default is "Linear".
Titles/Labels
The Titles/Labels option allows you to enter the title and labels for the graph. The Hershy character sets of 33 fonts are
used for plotting alphanumeric labels. Also, certain "special characters" may be embedded in the title or label which
control selection of alternate fonts or other aspects of the plotted text These special characters are not plotted, but are
interpreted as commands by the metacode translator software. The file HERSHY.BAR (included with the software)
contains the font information. See the appendices for more information on font selection codes.
Geo-EAS 1.2.1 14-6 XYGraph
-------
The screen fields accessed from this menu option are:
Main title An alphanumeric field which may contain up to 60 characters for the main title of the graph.
The default title contains the variable name selected as the post variable and the name of the
data file.
Subtitles Two alphanumeric fields which may contain up to 60 characters each for the subtitles on the
graph. The subtitles appear below the main title.
X Label Analphanumericfieldwhichmaycontainupto60charactersfprtheXaxislabeL Thedefault
label is composed of the X variable name followed by its units in parentheses.
YLabel Analphanumericfieldwhichmaycontainupto60characters,forthelabelontheYaxis. The
default label is composed of the Y variable name followed by its units in parentheses.
Reset
The Reset option allows the user to reset the parameters to their default values.
Geo-EAS 1.2.1 14-7 March 1991
-------
SECTION 15 CONREC
15.1 WHAT CONREC DOES
Conrec produces contour maps of variables with gridded coordinates in a Geo-EAS data file. The data must form a
complete grid. A grid is a a set of values with equally spaced X and Y coordinates which form a rectangle. Individual
grid cells may contain missing values. Default parameter values can be computed for all options, providing instant
results. Options allow control of contour levels, labeling, and smoothing. Options to control axes labeling and titles are
also available. A file called a "metacode" file is created for redisplay or producing a hardcopy.
15.2 DATA LIMITS
Conrec requires that the input data file contains at least three but not more than 48 variables. These should consist of
(at minimum) an X and Y coordinate, and a third variable for which contour lines will be drawn. The data file may contain
up to 10000 samples. These must form a grid with no more than 100 elements in each direction. If these limits are
exceeded the grid cannot be formed and the data file cannot be used by Conrec.
15.3 THE MENU HIERARCHY
Coorec
Prefix
Head Parameters
Option/Execute--
Save Parameters
\ Qett
Data
Variables
Qfaph Options
Contour Options •
Execute
X Quit
*. jcw*x *. «•*.*• • x+*rv*fH1p ^ .. ..
TttfesfLaiKjfe " ""^, ,s-
Spline
BditLevel* ' , - s
LabeMag s s\- :"*-
15.4 THE MAIN MENU
154
Conrec Main Screen
» rmi*:m-MX
-------
The Main screen and menu (Figure 15-1) has the options to allow specification of the input and output parameter file
names. The menu line appears as follows:
Prefix Read Parameters Options/Execute Save Parameters Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Read Parameters
The Read Parameters option is used to enter the input parameter file name.
Options/Execute
The Options/Execute option provides access to the Options menu. See the section on Options below for more
information.
Save Parameters
The Save Parameters option is used to enter the name of the output parameter file. The default output parameter file name
is the data file name with a ".cpf extension. If the file specified already exists, a Yes/No prompt for whether or not to
overwrite the file is displayed. This file will contain the current parameter values. It will be saved for future use as an
input parameter file.
15.5 THE OPTIONS MENU
'fi
/
A contouring vrogran for gridded data
Tile Fref Ix: C:\6eoEASVDaUS
Input ?araneter File :
Output ParMeter File:
Use this option to View the graph.
The plotting Instructions vlll be
saued In a special file called a
"Hetacode File". Other software
nay fee used to produce plotter
hardcow fro* this file.
Data File Hone: Exanple.grd
X Variable : Easting
1 Variable : northing
Contour Variable :
-------
Contour Options and Graph Options options will replace any previous entered values on these screens. If the response
is "No" and no contour levels have been set, an error message will occur when the Execute option is selected. The screen
fields accessed from this options are:
X Variable A toggle field for selecting the variable name whose values will be used as the X coordinates.
The default X variable is the first variable in the data file.
Y Variable A toggle field for selecting the variable name whose values will be used as the Y coordinates.
The default Y variable is the second variable in the data file.
Contour Variable A toggle field for selecting the variable name whose values will be used as the contour values.
The default Contour Variable is the third variable in the data file.
Graph Options
The Graph Options option provides access to the Graph Options screen and menu, described below.
Contour Options
The Contour Options option provides access to the Contour Options screen and menu, described below.
Execute
When the Execute option is selected, you will be prompted for a metacode file name. The metacode file is then created
and the graph is displayed. The metacode file name may be up to 14 characters. The default name is "METACODE.MET".
If the default value is not used and the file already exists, a Yes/No prompt provides an option to proceed or quit The
metacode file is stored on disk for later use. A hard copy of the graph can be obtained by using the program Hpplot and
an HPGL compatible plotter. If the number of contour levels is set to zero an error message is displayed. The user must
set the number of contour levels before the graph can be produced. Contour lines will not be plotted across a grid cell
which contains a missing value. After the graph (see Figure 15-3) has been displayed, type to clear the screen and
return to the Options menu.
Geo-EAS 1.2.1
15-3
Conrec
-------
15.6 THE GRAPH OPTIONS MENU
*<•'
''/
i *«
X Axis 1 Axis
Axes Parameters
Tick Parameters
1 (tajor Tlourk Divisions
1 Minor Divisions / Hajor
Tlcknark label ForMt
licnark Libel Size
Titles/Labels (lain
Full Full
6 5
2 Z
(FIB. 8) (Fie. 8)
3 3
Graph Units
X
Nin: 269.999
Max: 599.999
Size: 29.999
Center Subtitles: Center
(lain Title Kriging estlmtes produced fro* data file Example. gnt
Subtitles Contours for
-------
Titles/Labels
The Titles/Labels option allows you to enter the title and labels for the graph. The Hershey character sets of 33 fonts
are used for plotting alphanumeric labels. Also, certain "special characters" may be embedded in the title or label which
control selection of alternate fonts or other aspects of the plotted text. These special characters are not plotted, but are
interpreted as commands by the metacode translator software. The file HERSHY.BAR (included with the software)
contains the font information. See the appendices for more information on font selection codes.
The screen fields accessed from this menu option are:
Title Position Two toggle fields for selecting the position of the main title and the subtitles. The choices
available are "Left" (at the left edge), "Center" (centered on the line), or "Right" (at the right
edge). The default is "Center".
Main Title An alphanumeric field which may contain up to 60 characters, for entering the title of the
graph. The default title is the title from the data file.
Subtitles Three alphanumeric fields which may contain up to 60 characters each for entering the graph
subtitles. The default for the first subtitle is the name of the contour variable.
X Axis An alphanumeric field which may contain up to 60 characters for entering the X axis label.
The default X axis label is the X coordinate variable name.
YAxis
Size
An alphanumeric field which may contain up to 60 characters for entering the Y axis label.
The default Y axis label is the Y coordinate variable name.
Six toggle fields for selecting the character size for the labels. The choices available are "0"
to "10" where "0" is the smallest and "10" is the largest character size. The default for the
Main Title is "6". The default for the first and second subtitles and the X and Y axes is "5".
The default for the third subtitle is "4". These choices work well on the screen, however
smaller sizes might be more suitable for output to a plotter.
Annotation
The Annotation option allows the user to suppress the axes, tides, and labels for the graph. The screen field accessed
from this option is a toggle field that is displayed on the message line. The choices available are "Plot axes and titles",
or "No annotation" (do not plot axes and titles). The default is "Plot axes and titles".
15.7 THE CONTOUR OPTIONS MENU
'' ,?/ff' ' ys'i' /%"•"' ",,'' <
si ' SS.A ' '''*.''" ' •"
> #
""X
>'*
1
•>l
n
v.*v
Starting Contour Ualue .300
HaxiMiH Contour Ualue 2.4
Contour Level [ncrcnent .4
1 Contour Levels
Ubel ing Option Off
Ubel Skip factor 1
First Level to Ubel 1
Ubel Size 7
Dash Pattern : — —
lash Cutoff : .000
• Rep/Label : 5
Annotation Option: No Annotation
Character Size: 8
Contour Level
1 .090
2 .400
3 .800
4 1.200
S 1.600
6 2.000
7 2.400
8
3
10
11
12
13
14
IS
16
Ubel
.oesoer.oe
!aooooE01
.20000E*01
.24000E<01
;." New Levels Edit Levels Ubel Ing Dash Pattern illl'iMMII.f
|--; Select graph annotation options
Spline Quit
'.
The Contour Options screen and menu (Figure 15-5) has options to allow specification of the contour levels, labels, the
skip factor, label size and the selection of a dashed line pattern. The menu line appears as follows:
New Levels Edit Levels Labeling Dash Pattern Annotation Spline Quit
Geo-EAS 1.2.1
15-5
Conrec
-------
New Levels
The New Levels options allow you create a list of equally spaced contour values and labels. The defaults for these screen
fields may be calculated by the program when the Variables option is selected. The program calculates the contour levels
and the corresponding labels based on the values from these fields. The screen fields accessed from this option are:
Starting Contour Value A numeric field for entering the lowest contour level.
Maximum Contour Value A numeric field for entering the highest contour level.
Contour Level Increment A numeric field for entering the increment value between the contour levels.
Edit Levels
The EditLevels option allow you to change the contour labels or specify unequal contour level spacing. The screen fields
accessed from this option are:
Contour Level A column of numeric fields for entering the contour levels.
Contour Label An column of 16 character alphanumeric fields for entering the contour labels.
Labeling
The Labeling option allow you to select the contour labeling options. The screen fields accessed from this option are:
Labeling Option A two valued toggle field to enable or disable the labeling of contour lines. The choices
available are "On" (label contours) or "Off (do not label contours). If the Labeling Option
is "Off the other screen fields in this group are ignored. The default is "On".
Label Skip Factor A toggle field for selecting the skip factor for the contour labels. The Label Skip Factor
is the frequency at which to label the contour lines. For example if the Label Skip Factor is
two and the First Level to Label is 1 then contour levels 1, 3,5 ... would be labeled. The
choices available are "1" to "5". The default is "2".
FirstLevel to Label Aten-valued("l".."10")togglefieldforselectingthefirstcontourleveltolabel. Thedefault
is"l".
Label Size A ten-valued toggle field ("1".."10") for selecting the contour label character size. The
default is "6".
Dash Pattern
The Dash Pattern option allows specification of the Dash Pattern and the Dash Cutoff level. The screen fields accessed
from this option are:
Dash Pattern An alphanumeric field which may contain up to 12 characters, for entering the line pattern
to use for the contour line below the Dash Cutoff. The Dash Pattern is a combination of
characters and spaces with each non-blank character representing a solid line segment in the
Dash Pattern. The default is " ". The pattern " "would cause a solid
line to be plotted.
Dash Cutoff A numeric field for entering the Dash Cutoff value. If a contour level is below this value then
the line is plotted using the specified Dash Pattern.
# Rep/Label A toggle field for selecting the number of repetitions of the dash pattern between contour
labels to plot Choices available are "2" to "10". The default is "5".
Annotation
The Annotation option allows the specification of the graph annotation. The screen fields accessed from this option are:
Annotation Option A toggle field for selecting the type of graph annotation for the graph. The available choices
are "Plot Min/Max" and "No Annotation" (do not plot the minimum and maximums. The
default is "Plot Min/Max". If "Plot Min/Max" is chosen the minima and maxima of the
surface represented by the contour map will be plotted. An "H" denotes a local maximum
and an "L" denotes a local minimum.
Geo-EAS 1.2.1 15-6 March 1991
-------
Character Size A toggle field for selecting the character size to plot the graph annotation. Choices available
are "1" to "10". The default is "8". This value works well on the screen, however a smaller
size may be better suitable for output to a plotter. This field is ignored if the Annotation option
"No Annotation" is chosen.
Spline
The Spline option allows the specification of the amount of smoothing of the line segments. The screen field accessed
from tiiis option is a numeric field. Acceptable values range from 2.5 to 30. The larger the Spline Tension value the less
smoothing of the line. A value of 30 disables smoothing. Smooth contours generally look better, but because the contour
Geo-EAS 1.2.1 15-7 Conrec
-------
SECTION 16 VIEW
16.1 WHAT VIEW DOES
View displays on the screen the graphs contained in metacode files. The graphs can be displayed on a EGA, CGA, or
Hercules graphics system. Color graphs are viewed on EGA systems. On CGA and Hercules systems monochrome
graphs are displayed.
16.2 THE MENU HIERARCHY
View
Fife
Ssaie
Execute
\ Quit
16.3 THE MAIN MENU
The Main screen and menu, shown in Figure 16-1, has the options to allow specification of the metacode file name and
the plotting area. The menu line appears as follows:
Prefix File Scale Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
File
The File option is used to enter the metacode file name. The screen field accessed from this option is an alphanumeric
field and may contain up to 14 characters. This character string combined with the file prefix should form the name of
a valid metacode file, or an error is displayed. This file contains the metacode instructions produced by the programs,
Conrec, Xygraph, and Postplot.
16*1
A Metacnde translator for EGA, CGA, or Hercules graphics configuration
rile Prefix : C:v6eoEAS\D*ta\
Hetacodc Fl [ensue : netacnle.Kt
Scale : Square
Adaptor : EGA (646 x 356)
Execute
Use this option to display the
plot.
Prefix File Scale uHJJ.mj Quit
Display the plot
Geo-EAS 1.2.1
16-1
March 1991
-------
Scale
The Scale option is used to select the type of plotting area to use when displaying the graph. The screen field accessed
from this option is a toggle field. The choices available are "Square" (the original scaling of the graph), and "Rectangle"
(the graph will be stretched to fit the entire screen). The default is "Rectangle".
Execute
The Execute option is used to display the graph on the screen. When this option is selected the metacode file is read and
translated into graphic output for the type of graphic system in use. If a problem is encountered while trying to read the
metacode file an error message will be displayed. This can occur if the specified file is not in the correct format. The
metacode file can contain more than one graph (frame). To View subsequent frames press . After the graph has
been displayed, type to clear the screen to return to the Main menu.
Geo-EAS 1.2.1 16-2 View
-------
SECTION 17 HPPLOT
17.1 WHAT HPPLOT DOES
Hpplot translates the device independent plotting instructions in metacode files into a Hie of HPGL plotting commands.
The output file can be routed to a HP plotter by setting up the serial port (COM1) by running the batch file HPSETUP.B AT
and then using the DOS PRINT command to send the file to the plotter. The HP plotters supported are:
HP 7470- 2 pen plotter
HP 7475- 6 pen plotter
HP 7450- 8 pen plotter
If the HP 7470 is used for plotting the graph will be plotted in two pen colors, the program does not prompt for pen
changes.
17.2 THE MENU HIERARCHY
-Prefix
Fife
Scale
Execute
Quit
17.3 THE MAIN MENU
The Main screen and menu (Figure 17-1) has the options to allow specification of the metacode and output file names,
and the plotting area. The menu line appears as follows:
Prefix File Scale Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
' '"ttppfarf Mara Screen
Translates a netactxle file into HPGL plotting instruct I ores
File Prefix : C:\6eoEftSMtaUN
Input Filenue : Heticode.net
ttitnit PH#>MM^! ^nWffrSST^B
Scale: Square
Enter the output file wme
Prefix rile Scale Execute Quit
Geo-EAS 1.2.1
17-1
March 1991
-------
File
The File option is used to enter the metacode file name. The screen field accessed from this option is an alphanumeric
field and may contain up to 14 characters. This character string combined with the file prefix should form the name of
a valid metacode file, or an error is displayed. This file contains the metacode instructions produced by the programs
Conrec, Xygraph, or PostploL
Scale
The Scale option is used to select the type of plotting area to use when displaying the graph. The screen field accessed
from this option is a toggle field. The choices available are "Square" (the true scale of the graph), and "Rectangle" (the
entire screen). The default is "Rectangle".
Execute
When the Execute option is selected, you will be prompted for a output file name before the output file is created. The
output file name entered must be up to 14 characters. This file contains the instruction generated by translating the
metacode file into HPGL plotting instructions. If a problem occurs while accessing the metacode file an error message
is displayed. When execution is complete, the plot instruction file produced by Hpplot may be sent to an HP plotter or
compatible. This is accomplished by first running the DOS command file HPSETUP.B AT (provided with the software
distribution) to configure the COM1: serial port, and redirect printer output to COM1:. Type: HPSETUP . The
file may then be sent to the plotter by using the DOS command: PRINT {Filename} .
Geo-EAS 1.2.1 17-2 HPPlot
-------
APPENDIX A REFERENCES
Clark, I., 1979, Practical Geostatistics, Applied Science Publishers, London.
David, M., 1984, Geostatistical Ore Reserve Estimation, Elsevier, Amsterdam.
Isaaks, E.H and Srivastava, R.M., 1989, An Introduction to Applied Geostatistics, Oxford University Press, Inc.
New York.
Journel, A.G. and C.H. Huijbregts, 1978, Mining Geostatistics, Academic Press, London.
Rendu, J.M., 1981, An Introduction to Geostatistical Methods of Mineral Evaluation, South African Institute of
Mining and Metalurgy, Johannesburg.
Srivastava, R.M., 1988, "A Non-ergodic Framework for Variograms and Covariance Functions", SIMS Technical
Report No. 114, Dept. of Applied Earth Sciences, Stanford University.
Geo-EAS1.2.1 A-l References
-------
APPENDIX B NCAR GRAPH OPTIONS
The following is an excerpt from the NCAR Autograph Manual. It has been slightly modified to include the Tickmark
parameter names used in programs Xygraph and Postplot. This explanation may help to explain how these parameters
work together to produce numeric tickmark labels. Acceptable actual values for the screen fields are as follows:
No Labeling
Setting Label to 'None' turns off the numeric labels on the axis specified. The other parameters, are then ignored.
Scientific Labeling
Setting Label to 'Scien.' selects scientific notation. Each numeric label is written in the form:
[-] W [.] [fj * 10 e
Where brackets enclose portions which may be independently present or absent and 'e' is a superscript
exponent.
The value of the parameter Type is immaterial when scientific notation is selected.
The parameter Exponent specifies the number of character of 'i', thus also specifying the value of the exponent
'e'. IF Exponent has a value less than or equal to zero, 'i' is omitted. If Exponent is less than zero and has the
integral absolute value V, the fraction T is forced to have V leading zeroes.
The parameter Fraction specifies the number of characters in 'f . If Fraction is less than or equal to zero, ' f is
omitted. If Fraction is less than zero, the decimal point is omitted.
If "[i] [.] ffl" has the value '!.', the first part of the label is omitted, leaving only '10e'.
If the entire label has the value '0.', the single character '0.' is used.
Exponent Labeling
Setting Label to 'Expon.' selects exponential notation.
If the parameter Type has the value _ Base*k. Each numeric label is written in the form:
H[i][.]ffl*10e
Where brackets enclose portions which may be independently present or absent and 'e' is a superscript
exponent.
The parameter Exponent specifies the integral value of the exponent 'e'.
The parameter Fraction specifies the number of characters in T. If Fraction is less than or equal to zero, 'F
is omitted. If Fraction is less than zero, the decimal point is omitted.
If the label is exactly zero, the single character '0' is used.
If the parameter Type has the value _ Base*10Ak. Each numeric label is written in the form:
The parameter Exponent specifies the integral value of the exponent 'e' when 'k' equals '0.'. The value of 'e'
is Exponent plus 'k'.
The parameter Fraction specifies the number of characters in T . If Fraction is less than or equal to zero, T
is omitted. If Fraction is less than zero, the decimal point is omitted.
If the label is exactly zero, the single character '0* is used.
Geo-EAS 1.2.1 B-l NCAR Graph Options
-------
If the parameter Type has the value BaseAk. Each numeric label is written in the form:
[-] [il [.] [f] e
The parameter Exponent is ignored. The value of 'e' is 'k'.
The parameter Fraction specifies the number of characters in T. If Fraction is less than or equal to zero, T is
omitted. If Fraction is negative, the decimal is omitted.
(Note that '[i] [.] [f]' expresses the value of Base.)
Non-exponent Labeling
Setting Label to 'No-Exp.' selects non-exponent notation. The parameter Exponent is ignored.
If the parameter Type has the value _ Base*k. Each numeric label is written in the form:
[-] [i] [.] [f]
The parameter Fraction specifies the number of characters in T. If Fraction is less than or equal to zero, T
is omitted. If Fraction is less than zero, the decimal point is omitted. If the label is exactly zero, the single
character '0' is used.
If the parameter Type has the value _ Base* IC^k. Each numeric label is written in the form:
[-] [i] [•] [f]
The parameter Fraction specifies the number of characters in T when 'k' is zero .If Fraction is less than or equal
to zero, T is omitted. If Fraction is less than zero, the decimal point is omitted.
For example, if Fraction =1., Base = 3.6, and k ranges from -3 to +3; the labels produces are .0036, .036, .36,
3.6,36.360., and 3600.
If the parameter Type has the value _ BaseAk. Each numeric label is written in the form:
[-] [i] [•] [f]
if 'k' is greater than or equal to zero, and in the form
HI/raum
if 'k' is less than zero.
The parameter Fraction specifies the number of charactersin T when 'k' is equal to 1.. If Fraction is less than
or equal to zero,' f is omitted. If Fraction is less than zero, the decimal point is omitted. For example, if Fraction
= -1., Base = 2., and k ranges from -4 to 44; the labels produced are:
1/16,1/8,1/4,1/2,1,2,4,8,16
Geo-EAS 1.2.1 B-2 March 1991
-------
APPENDIX C HERSHY CHARACTER FONT TABLES
The Hershy character set consists of 33 different character fonts, numbered 0 through 32. This information is stored in
a machine-readable file called 'HERSHY.B AR', which is included with the software distribution. The font descriptions
indicate the extent to which the characters contain tapered segments (simplex, duplex, complex, triplex, or gothic), and
the size of the characters (cartographic, indexical, principal, or centered symbol). The following table lists available fonts
and font codes.
FONT DESCRIPTION
0 Cartographic Roman
1 Cartographic Greek
2 Simplex Roman
3 Simplex Greek
4 Simplex Script
5-6 Simplex Special Characters
7 Complex Roman
8 Complex Greek
9 Complex Italic
10-11 Complex Special Characters
12 Complex Roman
13 Complex Greek
14 Complex Italic
15-17 Complex Special Characters
18-19 Duplex Roman
20-21 Complex Script
22-23 Complex Cyrillic
24-25 Triplex Roman
26-27 Triplex Italic
28 Gothic German
29 Gothic English
30 Gothic Italian
31 Gothic Special Characters
32 Centered Symbols
Certain 'special characters' are used to inform the graphics software that this font information is to be used for plotting.
These characters may be embedded in graph titles or labels, and will allow selection of alternate font types, and other
special features. These special characters are not plotted, but are instead interpreted as commands by the metacode
translator software. The special characters and their meanings are:
" - backspace one character position
# - indicates a three-digit font selection code follows
% - selects the default font
< - subscript the next character
> - superscript the next character
The figure below illustrates the results of using the following five characters strings:
#004Geostatistical Environmental Assessment Software%
#027Geostatistical Environmental Assessment Software%
#007Geostatistical Environmental Assessment Software%
_Geostatistical Environmental Assessment Software_
Special characters - #003k%, #010Q%, #010t%, #008p%
Easting (M>2]
Geo-EAS 1.2.1 C-l Hershy Character Font Tables
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Figure C-l
Example font
selection codes
Font 004
Font 029
Font 007
Geostatistical Environmental Assessment Software
Underlining
Geostatistical Environf"fr"tfll Assessment Software
Special Characters from font 010 and font 008
Special Characters — y, <, s, i
Superscripting using the > character: Easting (m>2)
Easting (m2)
The following table illustrates all font groups, and symbols within each group:
Geo-EAS 1.2.1
C-2
March 1991
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APPENDIX D POLYGON FILE FORMAT
This section describes the format of a polygon file. They are used by program KRIGE to include or exclude computation of
estimates within specified polygonal areas. Polygon files are text files comprised of lists of X,Y coordinate pairs (vertices) which
form closed polygonal boundaries. These boundaries may be defined as inclusive or exclusive, meaning that estimates should
be excluded outside of inclusive boundaries, and included when outside of exclusive boundaries.
The Polygon File is processed in the following manner: Krige reads the specified polygon file before kriging and builds a matrix
of flags to indicate if point or block estimates are to be included or excluded. This matrix corresponds to the grid defined by the
user in the Krige Options Screen. Polygon files must be contracted with these grid boundaries in mind, because the grid and
polygon boundaries are related. As krige reads each polygon from the polygon file, each grid cell center is tested. If the cell center
(point or block center) is inside an inclusive polygon, (or outside an exclusive one) the corresponding flag is set to include the
estimate. Conversely, if a cell center is outside and inclusive (or inside an exclusive) polygon, the flag is set toexclude computation
of an estimate at that location. The rule which governs processing of multiple polygons is this: No flag may be changed to Include
an estimate which has been Excluded by a previous polygon, (for additional information see the Polygon option of Section 12).
Polygon files may contain an unlimited number of polygons. The first record (line) in the file should contain the number of
polygons contained in the file. Each polygon may be specified as an inclusive (Code 0), or exclusive (Code 1) polygon. A polygon
is specified by placing a polygon header record in the file, followed by no more than 100 polygon vertex records. A polygon header
record consists of two integers: The Include/ Exclude Code (0, or 1), followed by a comma, and the number of vertices
in the polygon. Exactly vertex records must follow. Each vertex record consists of two floating point (REAL) numbers
separated by a comma. These should be listed in an order such that straight lines connecting successive vertices would form a
closed polygonal boundary (if a final line were drawn from the last vertex to the first).
Polygon files may be created by any simple text editor such as the DOS editor EDLIN, or any word processor using non-document
mode. All lines in the file must be terminated with a CRLF (carriage-return line-feed). Below is an example of a polygon file
containing an inclusive square polygon, with an exclusive triangular polygon in the center.
2 Number of polygons
0,4 Inclusive, 4 vertices
0., 0. 1st vertex
0., 100. 2nd vertex
100., 100. 3rd vertex
100., 0. Last Vertex
1,3 Exclusive, 3 vertices
25., 25. 1st vertex
75., 25. 2nd vertex
50., 75. 3rd vertex
END OF FILE
*** Note *** No blank lines may be embedded in the file.
Geo-EAS 1.2.1 D-l Polygon File Format
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Dear Geo-EAS User:
Return this form to keep your name on the Geo-EAS mailing list so you can receive
future announcements on bugs, upgrades, etc. The information will help determine the
need for future maintenance and enhancements, establish development priorities, and to
define the types of computer systems we should support. Any additional comments on
Geo-EAS or information on your applications would be appreciated. Mail to:
Evan Englund
U.S.EPA EMSL-LV (EAD)
P.O. Box 93478
Las Vegas, NV 89193-3478
Yes, I want to be on the Geo-EAS mailing list.
NAME:
ADDRESS:
CITY: STATE: ZIP:
PHONE:
Type of Organization: Type of Applications:
U.S.EPA Superfund
Other Federal Government Other Environmental
State/Local Government Mining
EPA Contractor Research
Other Contractor/Consultant Short Courses
University/College College Courses
Industry Self-Instruction
Private Individual Petroleum
Other Other
Frequency of Geo-EAS Use: Programs Used Regularly:
Daily DATAPREP KRIGE
Weekly TRANS POSTPLOT
Monthly STAT1 XYGRAPH
Once or Twice per Year SCATTER CONREC
PREVAR VIEW
VARIO HPPLOT
XVALDD
How many copies of Geo-EAS have you distributed to others in your organization?
Outside of your organization?
(over)
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Briefly describe your Geo-EAS application(s):.
Comments on Geo-EAS (Past, Present, Future).
What kind of computer system (CPU, RAM, Operating System, Graphics) do you
expect to be using 2 or 3 years from now?
*US GOVERNMENT PRINTING OFFICE 1991-580-764