&EPA
United States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
P.O. Box 93478
Las Vegas NV 89193-3478
EPA/600/4-88/033
September 1988
Research and Development
GEO-EAS (Geostatistical
Environmental Assessment
Software)
User's Guide
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EPA600/4-88/033
GEO-EA8
(6EOSTATZ8TICAL ENVIRONMENTAL ASSESSMENT SOFTWARE)
USER'S GUIDE
by
Evan Englund
U.S. Environmental Protection Agency
Environmental Mentoring Systems Laboratory
Las Vegas, Nevada 89193-3478
Allen Sparks
Computer Sciences Corporation
4220 S. Maryland Parkway
La Plaza Bid. B, Suite 408
Las Vegas, Nevada 89119
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89193-3478
-------
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.
Geo-EAS 1.1 ii September, 1988
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ABSTRACT
This report describes how to install and use the Geo-EAS
(Geostatistical Environmental Assessment Software) software
package on an IBM-PC compatible computer system. A detailed
example is provided showing how to use the software to conduct a
geostatistical analysis of a data set.
Thirteen Geo-EAS programs are documented. The principal
functions of the package are the production of 2-dimensional
grids and contour maps of interpolated (kriged) estimates from
sample data. Other functions include data preparation, data
maps, univariate statistics, scatter plots/linear regression, and
variogram computation and model fitting. Extensive use of screen
graphics such as maps, histograms, scatter plots and variograms
help the user search for patterns, correlations, and problems in
a data set. Data maps, contour maps, and scatter plots can be
plotted on an HP compatible pen plotter. Individual programs can
be run independently; the statistics and graphics routines may
prove useful even when a full geostatistical study is not
appropriate. For ease of use, the programs are controlled
interactively through screen menus, and use simple ASCII data
files.
Geo-EAS 1.1 iii September, 1988
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Geo-EAS l.l iv September 12, 1988
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CONTENTS
Abstract iii
Contents v
List of Figures ix
Glossary xiii
Abbreviations xvii
Acknowledgments xix
1. Introduction 1-1
1.1 Overview 1-1
1.2 Equipment Requirements 1-2
1.3 Software Availability 1-3
1.4 User Profile 1-3
2. System Summary 2-1
2.1 Installing the System 2-1
2.1.1 The Distribution Diskettes 2-1
2.1.2 Hard Disk Installation 2-2
2.1.3 Using the Programs on Floppy Diskette . . . 2-2
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 2-3
3. System Operation 3-1
3.1 Data 3-1
3.1.1 Geo-EAS Data Files 3-1
3.1.2 File Naming Conventions 3-2
3.2 Interactive Screens 3-3
3.2.1 Screen Format . . 3-3
3.2.2 Types of Screen Input Fields. . 3-5
3.2.3 The Menu Tree 3-6
3.2.4 Common Menu Options 3-6
3.3 Geo-EAS Graphics 3-9
3.3.1 On-screen Graphics 3-9
3.3.2 Metacode-based graphics 3-9
3.4 Error and Recovery Procedures 3-10
4. Using Geo-EAS in a Geostatistical Study - an Example. . 4-1
4.1 Overview 4-1
4.2 Exploratory Data Analysis 4-2
4.3 Variogram Analysis 4-7
4.4 Kriging and Contouring 4-18
4.5 Summary and Excersises 4-24
Geo-EAS 1.1 v September, 1988
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Contents (continued)
5. DataPrep 5-1
5.1 What Dataprep Does 5-1
5.2 Data Limits 5-1
5.3 The Menu Hierarchy 5-2
5.4 The Main Menu 5-3
5.5 The DOS Utilities Menu 5-4
5.6 The File Operations Menu 5-7
6. Trans 6-1
6.1 What Trans Does 6-1
6.2 Data Limits 6-1
6.3 The Menu Hierarchy 6-2
6.4 The Main Menu 6-3
6.5 The Create Menu 6-4
6.6 The Operation Menu 6-5
7. Statl 7-1
7.1 What Statl Does 7-1
7.2 Data Limits 7-1
7.3 The Menu Hierarchy 7-1
7.4 The Main Menu 7-2
7.5 The Results Menu 7-4
7.6 The Histogram Options Menu 7-6
8. Scatter 8-1
8.1 What Scatter Does 8-1
8.2 Data Limits 8-1
8.3 The Menu Hierarchy 8-1
8.4 The Main Menu 8-1
9. Prevar 9-1
9.1 What Prevar Does 9-1
9.2 Data Limits 9-1
9.3 The Menu Hierarchy 9-1
9.4 The Main Menu 9-2
10. Vario -. 10-1
10.1 What Vario Does 10-1
10.2 Data Limits 10-1
10.3 The Menu Hierarchy 10-2
10.4 The Main Menu 10-2
10.5 The Options Menu 10-4
10.6 The Results Menu 10-7
10.7 The Lag Results Menu 10-9
10.8 The Variogram Modeling Menu 10-11
10.9 The Graph Options Menu 10-13
11. Xvalid 11-1
11.1 What Xvalid Does 11-1
11.3 The Menu Hierarchy 11-1
11.4 The Main Menu 11-2
11.5 The Options Menu 11-3
11.6 The Results Menu 11-9
Geo-EAS 1.1 vi September, 1988
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Contents (continued)
12. Krige 12-1
12.1 What Krige Does 12-1
12.2 Data Limits 12-1
12.3 The Menu Hierarchy 12-1
12.4 The Main Menu 12-2
12.5 The Options Menu 12-3
12.6 The Variables/Models Menu. 12-10
12.7 The Debug Displays 12-12
13. Postplot 13-1
13.1 What Postplot Does 13-1
13.2 Data Limits 13-1
13.3 The Menu Hierarchy 13-1
13.4 The Main Menu 13-2
13.5 The Graph Options Menu 13-5
14. Xygraph 14-1
14.2 Data Limits 14-1
14.3 The Menu Hierarchy 14-1
14.4 The Main Menu 14-2
14.5 The Options Menu . . . 14-3
14.6 The Graph Options Menu 14-6
15. Conrec 15-1
15.1 What Conrec Does 15-1
15.2 Data Limits 15-1
15.3 The Menu Hierarchy 15-1
15.4 The Main Menu 15-2
15.5 The Options Menu 15-3
15.6 The Graph Options Menu 15-5
15.7 The Contour Options Menu 15-7
16. View 16-1
16.1 What View Does 16-1
16.2 The Menu Hierarchy 16-1
16.3 The Main Menu 16-1
17. Hpplot ." 17-1
17.1 What Hpplot Does 17-1
17.2 The Menu Hierarchy 17-1
17.3 The Main Menu 17-1
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 1.1 vii September, 1988
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Geo-EAS 1.1 viii September, 1988
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LIST OF FIGURES
Number Page
2-1 GeoEAS System Menu 2-3
3-1 Example Interactive Screen 3-3
4-1 PostPlot Main Screen 4-2
4-2 Post Plot of Cadmium 4-4
4-3 Statl Main Screen 4-5
4-4 Statl Results Screen 4-6
4-5 Histogram of Cadmium 4-6
4-6 Cadmium Probability Plot 4-7
4-7 Prevar Main Screen 4-8
4-8 Vario Main Screen 4-9
4-9 Vario Options Screen 4-9
4-10 Variogram of Cadmium 4-10
4-11 Variogram with Model: Nugget=5,
Spherical, Sill=ll, Range=80 4-11
4-12 Variogram with Model: Nugget=5,
Spherical, Sill=ll, Range=100 4-12
4-13 Variogram with Model: Nugget=4.5,
Exponential, Sill=13.5, Range=160 ....... 4-13
4-14 Variogram with Exponential model, Lag
Spacing = 10 4-14
4-15 Variogram with Exponential model,
Lag Spacing = 25 4-14
4-16 Variogram, Exponential model, Lag Spacing 25,
Direction = 0 4-15
4-17 Variogram, Exponential model, Lag Spacing 25,
Direction = 45 " 4-15
4-18 Variogram, Exponential model, Lag Spacing 25,
Direction = 90 4-16
4-19 Variogram, Exponential model, Lag Spacing 25,
Direction = 135 4-16
4-20 Krige Main Screen 4-19
4-21 Krige Options Screen 4-19
4-22 Krige Variables/Models Screen 4-20
4-23 Contours for Cadmium Kriging Estimates. . . . 4-22
4-24 Contours for Cadmium Kriging Standard
Deviations 4-23
5-1 Dataprep Main Screen 5-3
5-2 Dataprep DOS Utilities Screen 5-4
5-3 Dataprep File Operations Screen 5-7
6-1 Trans Main Screen 6-3
Geo-EAS 1.1 ix September, 1988
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FIGURES (Continued)
Number Page
7-1 Statl Main Screen 7-2
7-2 Statl Results Screen 7-4
7-3 Statl Probability Plot 7-5
7-4 Components of a Box Plot 7-5
7-5 Statl Examine Screen 7-6
7-6 Statl Histogram Options Screen 7-6
7-7 Statl Histogram Results Screen 7-9
7-8 Statl Histogram 7-9
8-1 Scatter Main Screen 8-2
8-2 Scatter Scatter Plot 8-3
9-1 Prevar Main Screen 9-2
10-1 Vario Main Screen 10-2
10-2 Vario Options Screen 10-4
10-3 Illustration of Direction Parameters 10-5
10-4 Vario Post Plot 10-6
10-5 Vario Results Screen 10-7
10-6 Vario Variogram Box Plot 10-8
10-7 Vario Lag Results Screen 10-9
10-8 Vario Lag-Histogram 10-10
10-9 Vario Lag-Scattergram . 10-10
10-10 Vario Examine Lag Results Screen 10-11
10-11 Variogram Modeling Screen 10-12
10-12 Plot of Variogram with Model Curve 10-13
10-13 Variogram Graph Options Screen 10-14
11-1 Xvalid Main Screen 11-2
11-2 Xvalid Options Screen 11-3
11-3 Xvalid Search (and Variogram) Ellipse .... 11-4
11-4 Xvalid Kriging Display 11-8
11-5 Xvalid Results Screen 11-9
11-6 Xvalid Error Map 11-10
11-7 Xvalid Scatter Plot 11-10
11-8 Xvalid Error Histogram 11-11
11-9 Xvalid Examine Results Screen 11-12
12-1 Krige Main Screen 12-2
12-2 Krige Options Screen. . . . 12-3
12-3 Krige Kriging Display 12-9
12-4 Krige Variables/Models Screen 12-10
12-5 Krige Debug: Search Area Display 12-13
12-6 Krige Debug: System of Equations Display. . . 12-13
12-7 Krige Debug: Kriging Weights Display 12-14
13-1 PostPlot Main Screen 13-2
13-2 Example Post Plot 13-4
13-3 PostPlot Graph Options Screen 13-5
14-1 Xygraph Main Screen 14-2
14-2 Xygraph Options Screen 14-3
14-3 Xygraph Symbols and Line Types 14-4
14-4 Example Xygraph Plot 14-5
14-5 Xygraph Graph Options Screen. 14-6
Geo-EAS 1.1 x September, 1988
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FIGURES (Continued)
Number Page
15-1 Conrec Main Screen 15-2
15-2 Conrec Options Screen 15-3
15-3 Conrec Example Contour Plot 15-4
15-4 Conrec Graph Options Screen 15-5
15-5 Conrec Contour Options Screen ... 15-7
16-1 View Main Screen 16-2
17-1 Hpplot Main Screen 17-2
Geo-EAS l.l xi September, 1988
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Geo-EAS 1.1 xii September, 1988
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GLOSSARY OF GEOSTATISTICAL TERMS
Anisotropy - In geostatistics, the situation where a variogram
exhibits a longer range (i.e., better correlation) in one
direction than another.
Block Kriging - 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.
Covariance - 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.
Cross Validation - 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.
Discretization - In kriging, the process of approximating the
area of a block by a finite array of points.
Exponential Model - A function frequently used when fitting
mathematical models to experimental variograms, often in
combination with a nugget model.
Gaussian Model - A function frequently used when fitting
mathematical models to experimental variograms, often in
combination with a nugget model.
Geo-EAS 1.1 xiii September, 1988
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Glossary (Continued)
Geostatistics - 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.
Kriging - 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.
Kriging Standard Deviation - 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.
Lag - A distance class interval used for variogram computation.
Linear Model - A function frequently used when fitting
mathematical models to experimental variograms, often in
combination with a nugget model.
Madogram - 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.
Nested Variogram Model - 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.
Non-ergodic Variogram - 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. "Non-ergodic" is
a rather obscure term referring to the fact that some
probabilistic assumptions underlying the variogram
computation are no longer necessary. Non-ergodic variograms
may be modeled and used in kriging in the same way as
ordinary variograms.
Geo-EAS 1.1 xiv September, 1988
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Glossary (Continued)
Nugget Model - A constant variance model most often used in
combination with one or more other functions when fitting
mathematical models to experimental variograms.
Octant Search - 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.
Ordinary Kriging - 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.
Point Kriging - 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.
Quadrant Search - 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.
Range - 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.
Relative Variogram 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.
Geo-EAS 1.1 xv September, 1988
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Glossary (Continued)
Search Neighborhood - 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.
Semi-variogram - 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
"variogram11 for simplicity.
Sill - 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.
Simple Kriging - 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.
Spherical Model - A function frequently used when fitting
mathematical models to experimental variograms, often in
combination with a nugget model.
Variogram - 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 1.1 xvi September, 1988
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ABBREVIATIONS
Throughout this manual, keyboard keys are expressed in lower case
and enclosed in angle brackets. The following is a list of
commonly used keys:
SYMBOL
, , , , , , , , , ,
Geo-EAS 1.1
XVII
September, 1988
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Geo-EAS 1.1 xviii September 12, 1988
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ACKNOWLEDGEMENTS
This document is intended to serve both as an introduction to the
Geo-EAS software package (see Software Ordering Information,
Section 1.3), and as a reference manual. The Geo-EAS software
itself is, of course, the primary product, and deserves a brief
description of how it came about, along with an acknowledgement
of the many people who contributed to its development.
The ongoing USEPA research program in environmental geostatistics
at the Environmental Monitoring Systems Laboratory - Las Vegas
(EMSL-LV) was begun about six years ago, largely through the
efforts of George Flatman. As an incidental result of various
research projects conducted under Cooperative Agreements with
Stanford University, the University of Wyoming, and the
University of Arizona, EMSL-LV acquired a miscelleneous
collection of public domain geostatistical and 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
friendly1 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
feel1 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, also of CSC, converted public
Geo-EAS 1.1 xix September, 1988
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domain graphics routines from the National Center for Atmospheric
Research (NCAR) and used them to develop the Xygraph, and
Postplot programs. 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.
Evan J. Englund
Allen R. Sparks
Geo-EAS 1.1 xx September, 1988
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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 N02 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.
Geo-EAS 1.1 1-1 September, 1988
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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.
Geo-EAS 1.1 1-2 September, 1988
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1.3 SOFTWARE AVAILABILITY
The Geo-EAS software in its executable form is entirely in the
public domain, and can be obtained by sending the appropriate
number of diskettes (PREFORMATTED, PLEASE!) to the following
address:
Evan J. England (Geo-EAS)
USEPA EMSL-LV, EAD
P.O. Box 93478
Las Vegas, NV 89193-3478
The executable files and example data sets take approximately 3
megabytes of storage, and require the following number of
diskettes, depending on the type:
Type Number
5 1/4"
5 1/4"
3 1/2"
3 1/2"
1.2MB
360KB
1.44MB
722KB
3
9
3
6
The source code is written in FORTRAN 77 for the Microsoft
(Microsoft Corporation, Redmond WA) FORTRAN compiler (version
4.01). With the exception of slightly modified proprietary
Graflib (Sutra Software, Sugarland TX) subroutines used for
generating screen graphics, the source code is also in the public
domain. For further information on the source code and
programmer documentation, contact:
Geo-EAS
Computer Sciences Corporation
P.O. BOX 93478
Las Vegas, NV "89193-3478
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 use'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 1.1 1-3 September, 1988
-------
Geo-EAS 1.1 1-4 September, 1988
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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
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
Geo-EAS 1.1
2-1
September, 1988
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2.1.2 Hard Disk Installation
To install the system on a fixed disk, a subdirectory should
first be created (for example, GEOEAS). For information about
creating subdirectories, refer to the DOS reference manual. All
files on the distribution diskettes should be copied into the
subdirectory. For more information on how to copy files from a
diskette into a subdirectory, refer to your DOS user's manual.
Approximately three megabytes (3 million bytes) of storage 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.BAR. This means that if you only have 360 kilobyte disk
drives (and no fixed disk) you will not be able to use these
programs. A separate working diskette may be prepared for each
program, subject to the restrictions mentioned above.
2.2 INITIATING THE SYSTEM
2.2.1 Using the Geo-EAS system Menu
A program has been provided on the distribution diskettes which
allows access to 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 .
Geo-EAS 1.1 2-2 September, 1988
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*** 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-
resident programs, and re-start the computer. Programs in which
this is likely to happen are: Vario, Statl, Xygraph, and
Postplot.
c e o - E n s (i.u>
Geostat1st leal Enuiromental Assessment Software
Trans
Statl
Scatter
Preuar
Uarlo
Xualid
Xrige
Conrec
Xygraph
Postplot
HPplot
Uiew
Quit
Use arrou keys to noue cursor> to select progran
Data preparation utilities
Figure 2-1
GeoEAS System Menu
2.2.2
Using the Programs From DOS
To run the programs from DOS, type the program name at the DOS
prompt. For example, to start program Statl type: STAT1
Geo-EAS i.l
2-3
September, 1988
-------
Geo-EAS 1.1 2-4 September, 1988
-------
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 GeoEAS programs, as opposed to Pair Comparison
files, Parameter files, or Metacode files). Data files are
simple ASCII text files which may be created with any text
editor. It is 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
Geo-EAS 1.1 3-1 September, 1988
-------
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.
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
Northing
Arsenic
Cadmium
Lead
288.0
285.6
273.6
280.8
273.6
276.0
285.6
288.0
292.8
feet
feet
ppm
ppm
ppm
311.0
288.0
269.0
249.0
231.0
206.0
182.0
164.0
137.0
.850
.630
1.02
1.02
1.01
1.47
.720
.300
.360
11.5
8.50
7.00
10.7
11.2
11.6
7.20
5.70
5.20
18.25
30.25
20.00
19.25
151.5
37.50
80.00
46.00
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
Geo-EAS 1.1 3-2 September, 1988
-------
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 PREVAR, read by VARIO
.GRD - a gridded Geo-EAS data file (could be produced by KRIGE)
.CPF - CONREC parameter file
.KPF - KRIGE parameter file
.XPF - XYGRAPH parameter file
.POL - Polygon boundary file, used by KRIGE
.MET - metacode (graph) file, created by CONREC, POSTPLOT, and
XYGRAPH, and used by HPPLOT, and VIEW
.PLT - plotter instruction file, produced by HPPLOT
3.2 INTERACTIVE SCREENS
3.2.1 Screen Format
All Geo-EAS programs have similar interactive features. Each
program uses interactive screens for selection of program options
and display of results. The screens are composed of several
common components. Figure 3-1 displays an example interactive
screen from program Statl. Below is a description of the common
components.
(A.) A program to compute uniuariate descriptive statistics
File Prefix: C:\GeoEAS\Data\
File
Data File Nam
Variable
Variable
Ueijht
Log Option
Units
NinlMin
Haxinun
: Exanple.dat
: Cadniun ( D )
: None ^-/
: Off
: .888
: 16.788
t Variables
• Data records
• Hissing Data
Exacu
Use this option t
display the stati
of additional gra
will be displayed
5
68
8 <2
Obs<=8)
te
o compute and
rtlcs. A Menu
phs and options
(B)
Prefix Data Uariable Units
Compute basic descriptive stats
Batch Statistics Quit
Figure 3-1
Example Interactive Screen
Geo-EAS 1.1
3-3
September, 1988
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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 Statl
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 1.1 3-4 September, 1988
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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 Statl screen:
Alphanumeric Fields - These fields may contain character
strings of alphabetic or numeric characters. Any
alphanumeric characters may be entered. The "Prefix", and
"Data" menu options in Statl require alphanumeric values to
be entered. To specify a data file name, select the Data
option on the menu, and type the name of the input data
file.
Numeric Fields - Only numeric data may be entered into numeric
fields. Some numeric fields will only accept integer (non-
decimal) numbers. The programs will respond to any
erroneous keystrokes (such as alphabetic keys) with a low-
pitched error tone. An example of numeric fields in program
Statl are the two fields accessed through the Limits option
Only numeric values may be entered into these fields.
Values must be entered in the conventional manner (legal
characters are <0> through <9>, and <•>, exponential
notation for numeric values is not allowed.)
Toggle Fields - A toggle field is a special type of field which
contains a list of 2 or more preset choices. Only one of
these choices is displayed in the field. The key is
used to change the displayed choice, and the key is
used to make the selection. Two examples of toggle fields
in program Statl are the "Variable" field and the "Log"
field. Once a file name has been specified, the "Variable"
toggle field will contain the names of all variables in the
file. When the Variable option, on the menu line is
selected, this field will be highlighted, and each time the
key is pressed, a new variable name will appear in
the field. When the desired variable name appears, press
the key to select it. The "Log" field is an example
of a toggle field with only two choices ("On", or "Off").
If "On" is chosen, then statistics will be calculated for
the log of the selected variable.
Yes/No prompts, prompts for additional information - These
prompts are for information which will not be displayed
permanently on the 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 the "Do you really want to Quit
?" prompt which is displayed after the "Quit"
(terminate program) option is selected. Some menu choices
will result in prompts for additional information. These
prompts for additional information will appear on the
message line and may be of the alphanumeric, numeric, or
toggle type.
Geo-EAS 1.1 3-5 September, 1988
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3.2.3
The Menu Tree
The programs in the Geo-EAS system require input typically from
data files and through interaction on the screen. These program
inputs are arranged in a hierarchy of functionally-related
groups. Each group, or individual program parameter value is
accessed through a menu of choices. Some choices will lead to
other menus, while some will lead to prompts for groups of one
or more inputs. Such an arrangement can be represented in a
"menu tree" as illustrated below for program Statl.
Example menu tree
Statl
Prefix
Data
Variable
Limits
Execute -
Histogram
Type
Class Limits
Axes
Title
Results
View Graph
\ Quit
Probability Plot
Examine
\ Quit
Batch Statistics
V Quit
In the Statl menu tree, as in other programs, some menu choices
will lead to program inputs, and some will produce numeric or
graphical results. This hierarchy of options and results is a
natural and convenient way of providing choices for program use,
The "menu tree" representation of program options provides a
"road map" for each program which summarizes the functional
capabilities of a program. You may explore the hierarchy of
options by traversing the menu tree and reading the descriptive
messages which appear.
3.2.4
Common Menu Options
Many of the programs in the Geo-EAS system share common menu
options. These will be discussed in this section to avoid
redundancy. Any minor differences which apply to a particular
program will be discussed later in detail. The following is a
list of options common to many programs:
Geo-EAS 1.1
3-6
September, 1988
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Prefix
This option is common to all Geo-EAS programs. It is used to
specify a string of up to 50 alphanumeric characters which are
used as a prefix for all files accessed by a program. Typically,
it is used to include a disk drive and/or a directory
specification. Before a file is accessed by a program, a file
name is constructed which consists of the File Prefix followed by
the given file name. File name errors are not caught by the
programs until they have attempted to access a file.
Consequently, "file not found" error messages are not issued
until an attempt to access the file has been made. This may be
due to a mistake in the file prefix or file name specified.
Data
This option is common to most Geo-EAS programs. It is used to
indicate the Geo-EAS input data file to be used by the program.
File names consist of 14 alpha-numeric characters. Any valid DOS
file name may be used. The File Prefix (discussed above) is used
to construct the entire file name when the file is accessed by
the program. If any errors occur while the programs are
accessing or reading a data file a message indicating the problem
will be issued. If a "file not found" message is displayed, the
problem may be with the file prefix (see above). If no errors
occur, the variable names are read from the data file and stored
into toggle fields for use by the Variables option.
Variable(s)
This option is common to all programs which use Geo-EAS data
files. It allows you to specify the variable (or variables)
which the program will use. Some programs only use one variable
(e.g. Statl) and others require three (e.g. CONREC). Typically,
this option will provide access to one or more toggle fields
which contain the variable names. Some programs include
additional fields for selection of other parameters related to
the choice of variables. These will be explained in the
particular section which describes the program.
Execute
This option is common to all Geo-EAS programs. It is used to
initiate 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
Geo-EAS 1.1 3-7 September, 1988
-------
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.
Geo-EAS 1.1 3-8 September, 1988
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3.3 Geo-EAS GRAPHICS
3.3.1 On-Screen Graphics
Many Geo-EAS programs have graphics capability. Each such
program uses graphics in one of two ways. Programs Statl, Vario,
Xvalid, and Krige plot graphics directly on the screen. This
approach is used to provide a quick look at data, or program
results. Such graphics displays may be printed 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 graphics printer. 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 the 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 1.1 3-9 September, 1988
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3.4 ERROR AND RECOVERY PROCEDURES
Normal Error Processing
A great deal of effort has been put into error checking into the
programs. This includes bounds checking on numeric parameters,
file names, file Input/Output, and file existence. When errors
of these types are encountered in programs, error messages are
displayed on the message line at the bottom of the screen. These
messages are displayed in a black-on-white format (reverse). A
typical error message is "Error encountered while reading data
file...(press any key)". These messages will remain on the
screen until a key is pressed. To return to the interactive
screen after such a message is displayed, press any key.
Bugs
As everyone knows, people make mistakes. Because computer
programs are designed by people they usually contain mistakes,
or errors in program(mer) logic called "bugs". The Geo-EAS
programs have been extensively tested, and many bugs have been
uncovered and corrected. No known bugs have been allowed to
remain, however it is entirely possible that there are still a
few bugs lurking in the depths of some of the programs. It is
still possible that there are situations which will cause some
programs to "crash", or "fail" (terminate prematurely), or to
"lock-up" (pause indefinitely with no response). If a program
"locks-up", the computer system must be re-started. It may be
due to a bug, or due to a printer or disk-drive problem (see
below) If a program terminates prematurely it is probably due to
a bug.
Bug Reporting (how you can help):
If you encounter a problem and you think it may be a significant
bug, a bug report would be greatly appreciated. When you
suspect a bug and want to report it, there are several steps that
you should take: First, you should try to reproduce it (make it
happen more than once). If a bug is not reproducible, it will be
very difficult to determine the cause. Secondly, you should make
note of the exact sequence of inputs which caused the problem,
including your hardware configuration (if known). This
information should be included on paper or diskette along with a
description of the problem, so that the bug nay be corrected. A
detailed description and all program inputs will allow the
programmers to reproduce the error and solve it more quickly.
Every effort will be made to correct significant program errors
as soon as possible. Check the READ.ME file in the software
distribution, where known bugs may be. reported.
Geo-EAS 1.1 3-10 September, 1988
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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 1.1 3-11 September, 1988
-------
Geo-EAS 1.1 3-12 September, 1988
-------
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
5
Easting
Northing
Arsenic
Cadmium
Lead
288.0
285.6
273.6
280.8
feet
feet
ppm
ppm
ppm
311.0
288.0
269.0
249.0
.850
.630
1.02
1.02
11.5
8.50
7.00
10.7
•
18.25
30.25
20.00
19.25
Geo-EAS 1.1 4-1 September, 1988
-------
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:\GEOEAS> 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.
ft progran for plotting 2D sanpte locations and ualues
File Prefix: C^GeoEflSMtata^
Data : Exanple.dat
Uar tables
X coordinate uariable Easting
V coordinate uariable Northing
Uariable to post Cadniun
Options
Include Ualues = No Size = 5
Scale Factor = IB" 8
n Decimals : 1
Include Synbols: Ves Size : 4
Hetacode File : Netacode.net
Execute
Use this option to create the
plot. The plot ulll be sawed in
the file specified.
—
Prefix Data Variables Options Graph Options
Generate the plot
Quit
Figure 4-1
PostPlot Main Screen
The bottom line on the screen provides the list of available
options. The first five move you to an area on the screen (or to
a new screen) where you can input or select program parameters.
The Execute option starts the actual processing portion of the
program, and Quit moves you to the preceding menu (or out of the
Geo-EAS 1.1
4-2
September, 1988
-------
program). AH 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.
*** NOTE *** Whenever feasible, the programs will use
default options and values. These may be preset, computed
from the available data, or passed from a previously run
program. Be careful! The computer doesn't understand your
problem or your data. Defaults make it easy to get a result
quickly, not necessarily to get an appropriate result. In
this example we will usually use the defaults to get quick
results. Try other options to get familiar with the full
range of system capabilities.
In Postplot, the minimum that you MUST do to obtain a plot is:
1. Use the Data option to enter the name of a Geo-EAS data
file (or accept the default name, if one is provided).
2. Use the Variable option to select the X and Y variables
and the desired variable for posting (or accept defaults).
3. Use the Execute option to enter a name for the metacode
file (or accept the default), create the metacode file, and
display the map.
In this case you can skip the Prefix option because the data file
is in the Geoeas directory, and enter the file name Example.dat
with the Data option. The program reads the data file, and
automatically 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:
Geo-EAS 1.1 4-3 September, 1988
-------
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
Mecode.met
Y
The resulting Post plot is shown in Figure 4-2.
Postplot of Cadmium from dota fT1« Examplc.dat
ZOO
I
s
20O
1OO
x
X
-565-
BOO
1>i Ouortila:
2nd Cuarb'to:
3rd Ouartila:
4th Ouartll*:
Eavting (fact)
.OOO f +
5.300 < X
7.600 < D
10.800 < *
9.3OO
7.600
10.000
10.700
Figure 4-2
Post Plot of Cadmium
From this plot you can see that the samples fall in a rectangular
area about 250 by 220 feet. The sample locations are irregularly
spaced, and although there are some.gaps and clusters, they
provide relatively uniform coverage over the entire rectangle.
The symbols/colors represent the quartiles for the cadmium
values, with */red as the upper guartile, 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.
Geo-EAS 1.1
4-4
September, 1988
-------
*** 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 Statl to generate some statistics on
the data. When Statl is initiated, the Main screen will be
displayed as in Figure 4-3.
ft progran to conpute unl war late descrlptlue statistics
File Prefix: C'XIeoEASMIatav
File
Data File Mane : Exanple.dat
Uar table
Uarlable '• Cadnlun
Uelght : None
Log Option : Off
Units
flininun : .889
Haxinun : 16.788
1 Uarlables = 5
B Data records : 68
B Hissing Data : B (2
Execute
Use this option to ampul
display the statistics.
of additional graphs and
uill be displayed.
Obs<=8)
te and
ft itenu
opt ions
Prefix Data Uarlable Limits
Conpute basic desertptiue stats.
Figure 4-3
Htra Batch Statistics Quit
Statl Main Screen
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
FIELD
VALUE
DATA
VARIABLE
EXECUTE
HISTOGRAM
Accept
Select
Accept
Accept
Data File
variable
weight
log option
Example.dat
Cadmium
None
Off
QUIT
PROB.PLOT
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.
Geo-EAS 1.1
4-5
September, 1988
-------
Data File : C'MtojEflSMIata^Exanple
Uarlable : Cadnlun
Lower Linlt :
Upper Linlt : 16
B Obseruations 68
B Hissing Data 8
B Retained 68
Mean
Uar lance
Std. Deviation
xCoef. Uarlation
Skeuness
Kurtosis
.098
.788
7.8858
15.5315
3.9418
49.9889
-.1518
2.4639
.dat
Sun of Heights
Hinlnun Ualue
25 th Percent lie
Median
75th Percent lie
Haxinun Ualue
68.8888
.8888
siseee
7.6888
18.8888
16.7888
Probability Plot Exaiilne Quit
Choose histogran parameters / display graph
Figure 4-4
Statl Results Screen
Hlstogra-ax
Data file: Exaxplv.dat
9. •
0 '• '
e
a
9
i
3.
B •
•«•
•""
>_
—
""""
^
—
1
e. 4. t. 12.
CajMlun <»PM>
__
1 N Total 68
n
N Miss B
N Used 68
Mean 7.885
Variance 15.531
Std. Dev 3.941
ft C.V. 49.981
Skeuness -.151
Kurtosis 2.464
Mlninun .888
25th ft 5.388
Median 7.688
75th X 18.888
Haxinun 16.788
J.C. 88.
Figure 4-5
Histogram of Cadmium
Geo-EAS 1.1
4-6
September, 1988
-------
NOTM*! Probability Plot for Cadnlun
Data fil»: Exanplc.dat
s
1
« 8
X
S
.,«•
V"
^
/
/"*
»**
t
Statistics
N Total 68
H Hiss 8
N Used 68
Mean 7.885
Variance 15.531
Std. Dew 3.941
* C.V. 49.981
L Skeuness -.151
Kurt os is 2.464
a ninlnun .888
25th % 5.388
Median 7.688
75th % 18.888
naxinon 16.788
1 18 39 30 70 90 99
CuMulatlv* P*po*nt
Figure 4-6
Cadmium Probability Plot
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.
4.3
VARIOGRAM ANALYSIS
The computation, interpretation, and modeling of variograms is
the "heart" of a geostatistical study. The variogram model is
your interpretation of the spatial correlation structure of the
sample data set. It controls the way that kriging weights are
assigned to samples during interpolation, and consequently
controls the quality of the results.
All interpolation and .contouring methods make the assumption that
some type of spatial correlation is present, that is, they assume
that a measurement at any point represents nearby locations
better than locations farther away. Variogram analysis attempts
to quantify 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
Geo-EAS 1.1
4-7
September, 1988
-------
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.
ft preprocessor for progran UAR 10
File Prefix1 C:V5eoEASMIataN
Files
Data Flle: Exanple.dat
Pair Conparison File: Exanple.pcf.
Uar tables
X Uar table: Easting
Y Uar table: Northing
Units
ntninun llaxinun
X: 254.488 492.888
y: 118.888 315.888
Distance: .888 388.647
Uar tables 5
Records 68
Pairs possible 1778 nax:16384
Execute
Select this option to build the
pair conparison file. Distances
and directions for all pairs will
be conputed (subject to Units) •
sorted by d istances i and saved.
Prefix Files Variables Units
Build the pair conparison file
Figure 4-7
Quit
Prevar Main Screen
The option sequence below creates the pair comparison file
Example.pcf.
OPTION
FILES
ACTION
Accept
Accept
FIELD
Data File
Pairs File
VALUE
• Example.dat
Example. pcf
EXECUTE
QUIT
Answer
Next, initiate Vario, and the Vario Main screen is displayed, as
in Figure 4-8.
Geo-EAS 1.1
4-8
September, 1988
-------
A progran Tor conputlng uarlograns
File Prefix :C:NCeoEftSM)ataN
File
Pair Conparison File: Exanple.pcf
Uariable
Uarlable-' CadnJun
Log Option: Off
Linits
tlininun: .888
tlaxinun: 16.788
Uars : 5 I Kept
Data : 68 8 Obs<=8
Pairs: 1778 a Hissing
Uariogran Options
Use this option to displa
Uariogran Options Screen
Uariogran options nay be
and the uariogran nay be
68
2
8
y the
and nenu.
selected
conputed .
Prefix Data Uariable Linits
Quit
Specify uariogran optionsi conpute
Figure 4-8 Vario Main Screen
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
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.
1 EXU
Uariable :Cadnlun
ninlnun •' ,888
Haxinun : 16.7
Direction
Direction : .888
Tolerance : 98.888
rtax Banduldth: MAX
Lag Spacing
Hininun : .888
Haxinun : 158.888
Increnent : 15.888
Las
1
2
3
4
5
6
7
8
9
18
11
12
Pair File Exanple.pcf
nin. Distance 6,88
flax. Distance 382.
Distance Lag Distance
15.888
38.888
45.888
68.888
75.888
98.888
185.888
128.888
135.888
158.888
13
14
15
16
17
18
19
28
21
22
23
24
Direction Hew Lags Change Lags liflHBiifill Execute Quit
Uleu a post plot of data
Figure 4-9
Vario Options Screen
Geo-EAS 1.1
4-9
September, 1988
-------
First, specify the distance class intervals (lags) and
directional tolerances for computing the variogram. Finding the
"right" combination is a trial and error exercise, but a
systematic approach can be helpful:
To start, you will use the default direction, which is an
"omnidirectional" variogram. The angular tolerance of 90 degrees
on either side of any specified direction line allows all pairs
to be included regardless of direction. This maximizes the
number of pairs in each distance class, which usually gives the
"best" or smoothest variogram. See Figure 10-3 in Section 10 for
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. The maximum pair distance
is therefore divided by two, and then subdivided into ten equal
distance classes. Round these to the more convenient numbers of
150 and 15, and plot the resulting variogram (Figure 4-10), as
follows:
OPTION
NEW LAGS
ACTION
Accept
Input
Input
FIELD
Minimum
Maximum
Increment
VALUE
0
150
15
EXECUTE
PLOT
11.
19.
S 11.
s
•J ».
4
t.
i. '
•
"•"•— '« *— —
i • * i
i •
.
,
•
«ja. ••. iaa. it
Pll. <
Pairs :
Dlract.:
Tol. :
ItaxBand:
Caiktlun
nininun:
Hailnun:
Haan :
War. :
• .
Cxaxpla.pcf
1242
.886
seiaee
n/m
Llnl*.
.eee
16.788
7.885
15.531
Figure 4-10 Variogram of Cadmium
Geo-EAS 1.1
4-10
September, 1988
-------
This variogram shows a well defined structure. Except for the
fifth point, which is too low, the shape is typical of a
"spherical" model variogram, i.e., an initial linear increase
from the Y-intercept curving relatively sharply into a horizontal
constant value. The spherical type of variogram is observed
frequently in experimental variograms, and is one of the model
options available in Geo-EAS. To fit a spherical model to a
variogram, you need to estimate the "nugget" or Y-intercept, the
"sill" or difference between the nugget and the maximum value,
and the "range" or distance at which the model reaches the
maximum value. With a little practice, good fits can usually be
obtained within two or three tries.
Try an initial model with a nugget of 5, a sill of 11, and
a range of 80, using the following option sequence (Note that
after variogram model parameters have been entered, the
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
PLOT
Input
Toggle
Input
Input
Nugget
Type
Sill
Range
Spherical
11
80
UapiosiPAH fop CadniUH
Par
18.
IS.
£ 12.
a
e
9.
fc
4
9
6.
3. •
8 '
;S^ " *
/* *
/
/*
S^
f
/
/
File
Pairs
Direct.
lol.
HaxBand
Cadnlun
ninlnun
tlaxinun
(lean
U«r-
a. 40. eg. 120. i<0.
Dl>tmno»
a n e t e r s
:Exanple.pcf
: 1242
: .888
: 98.888
: n/a
Llnits
: .888
: 16.788
: 7.885
: 15.531
Variogram with model: Nugget=5, Spherical,
ll, Range=80
Figure 4-11
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:
Geo-EAS 1.1
4-11
September, 1988
-------
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.
Uarlogrrax for C«AniuM
Par
18.
13.
J 12.
L
0
- 9. •
fc
«
9
6.
3. •
o •
S^*^ "
jS
.s
/
jf
^r
y
*T
'
File
Pairs
Direct.
Tol.
MaxBand
Cadnlun
Mininun
flaxinun
tlean
U»F-
a. 48. 80. 120. 168.
Distance
:ExanpIe.pcf
: 1242
: .888
: 98.888
: n/a
Llnits
: .888
: 16.788
: 7.885
: 15.531
Figure 4-12
Variogram model: Nugget=5, Spherical,
ll, Range=100
This is an excellent fit; about as good as you can get with a
spherical model. That low fifth point, however, suggests that an
exponential model which has a more gentle 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.) A bit of
trial and error leads to an exponential model with a nugget of
4.5, sill of 13.5, and range of 160. This graph is displayed in
Figure 4-13.
OPTION
-ACTION
FIELD
VALUE
MODEL
PLOT
Input
Toggle
Input
Input
Nugget
Type
Sill
Range
4.5
Exponential
13.5
160
Geo-EAS 1.1
4-12
September, 1988
-------
Uar>lovi>an fop
18.
IS.
12.
9.
6.
3.
0.
0.
40. ee.
Dlct«nc*
120.
Paraneters
File
Pairs
Direct.
lol.
HaxBand
Cadniun
nininun
Haxinun
tie an
War.
Exanple.pcf
1242
.888
98.888
n/a
Liniis
iioa
• CXTO
16.788
7.885
15.531
160.
Figure 4-13
Variogram with Exponential model: nugget=4.5,
Sill=13.5, Range=160
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.
OPTION
ACTION
FIELD
VALUE
QUIT
QUIT
NEW LAGS
EXECUTE
MODEL
PLOT
Accept
Accept
Input
Minimum
Maximum
Increment
0
150
10
Geo-EAS 1.1
4-13
September, 1988
-------
«•»!••?•» for
(*•!••„. t.r«
Fll. iCunpU.pcf
Fair* : 1242
:t.:
Din
lol. :
ru«B«nd:
Cadnlun Llxlti
fllnlmm:
ttoxlnun:
.888
98.888
Vw.
16.1
7.883
15.531
Figure 4-14 Variogram with Exponential Model, Lag Spacing=10
Now repeat the above option sequence with a lag increment of 25.
The resulting graph is displayed in Figure 4-15.
I*.
1*.
IS.
A .
p •
Fll.
rain
itxanpU.pcr
: 1242
Dlraet.:
lot. :
lUxBand:
Cadnlun Llnltm
rUnlnun:
rtaxtnun:
rtean
War.
16.788
7.885
15.531
Figure 4-15 Variogram with Exponential Model, Lag Spacing=25
As you can see, the ability to define the "true" variogram
structure is limited by the particular set of data available.
The best you can do is to find a model which fits reasonably well
over a range of lag spacings. Both of the two models proposed
earlier are satisfactory. In practice, kriging estimates
calculated with the two variogram models will be almost
identical. Kriging standard deviations however, are more
sensitive than the estimates to changes in the variogram model,
as well as to differences between the "real world" and the
assumptions underlying the kriging equations. For this reason,
it is generally not wise to interpret kriging standard deviations
as a true measure of the estimation error. For the remaining
discussion of 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
Geo-EAS 1.1
4-14
September, 1988
-------
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
11.
».
5
1.
ft
•
i *•'
3
•|f
*
/I
.
m m
'
«a. ma. na. 14
Pile
Pair*
Dlraet
lol.
naxBan
Cadnlu
ninimi
na>lnu
Hean
War.
1.
tEjcanple.pcf
: 332
. i .eee
: 22. see
dt nf*
n Llnlta
n: .888
n: 16.788
: 7.885
: 15.531
Figure 4-16 Variogram , Exponential Model, Direction = 0
Vmrtmtrmm tmr
Pair* :
Direct.:
Tot. :
384
4S.B88
22.see
Lin It*
Illnlmjn:
Hnlnwi:
••. ia«. i*».
»t«t ajtc*
War. :
16.708
7.883
IS. S3!
Figure 4-17 Variogram, Exponential Model, Direction=45
Geo-EAS 1.1
4-15
September, 1988
-------
•a.
»l«t*ne«
Pair* :
Olract.:
Tol. :
na»Band:
312
se.eea
22.5W
Unit*
ninlnun:
naxlnun:
War.
16.1
7.885
IS.531
Figure 4-18 Variogram, Exponential Model, Direction=90
34.
2O.
It.
12.
t.
File iCxanpla.per
Pair* : 29
Direct.:
lot. :
135.888
22.SOB
n/m
Cadnlun Unit.
ninlnun:
naxlnun:
IS.7M
7.885
IS. 531
Figure 4-19 Variogram, Exponential Model, Direction=135
These four variograms provide a good illustration of why you
usually model the omnidirectional variogram first. In the
directional variograms, most of the definition of shape, nugget,
and sill has been obscured. You can see, however, a general
confirmation of the assumption about the anisotropy. The points
on the 0 degree variogram all fall below the omnidirectional
model, suggesting the range in that direction should be longer.
The opposite is true for the 90 degree variogram, while the 45
and 135 degree variograms are reasonably well 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 major 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.
Geo-EAS l.l
4-16
September, 1988
-------
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
"mad'ogram" 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.
Geo-EAS 1.1 4-17 September, 1988
-------
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 10x10
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 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) .
Geo-EAS 1.1 4-18 September, 1988
-------
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 progran for kriging a grid of estimates
File Prefix:
Read Paraneter File
Input
Paraneter FIle Exanple.Kpf
Saue Parameter File
Output
Paraneter File: Exanple.Kpf
Paraneter files are used to saue
and retrieue kriging parameters.
The BEAD option allows previously
SAUEd options to be retrieved fro*
the Input Paraneter File.
Prefix JE
Options/Execute Saue Parameters Quit
Read progran parameters
Figure 4-20 Krige Main Screen
Title' Exanple.grd - krlged estinates of data fron Exanple.dat
Data
Data File : Exanple.dat
Output File : Exanple.grd
Polygon
Polygon File:
Type
Type of Kriging : Ordinary
Point or Block : Block 2x2
Grid Paraneters
X V
Uarlable Easting Horthing
Origin 268.888 128.888
Spacing 28. 888 28.888
Nunber " 13 11
Search Paraneters
Hajor Radius : 59.488 i Sectors :
Hi nor Radius : 59.488 flax in Sector:
Ellipse Angle: .gee din. to use :
Distance Type: Euclidean Enpty Sectors:
1
8
1
8
Data Polygon Type Grid Search .Utnt1.1t4.-aiiriTirgia Title Execute Quit
This option invokes the Uariables and Uariogran Models screen
Figure 4-21 Krige Options Screen
Use the following option sequence to specify the file names and
grid parameters, and to proceed to the next menu (Figure 4-22):
Geo-EAS l.l
4-19
September, 1988
-------
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 I cells
Example.dat
Example. grd
Easting
Northing
260
120
20
20
13
11
VARIABLES/MODELS
List
of
Variables
to
Krige
1 Cadniun 3
2
3
4
6
7
8
9
IB
Uariable • Cadniun
Uariogran Model Paraneters
B Type Sill Ualue
1 Exponent. 13.588
2
3
4
Global Mean :
Hugget : 4.588
tlajor Range Hi nor Range Angle
JtitJ • MM loo t MM • HBcJ
Neu Uariable iCTH Delete Quit
Select a uariable and edit the uariogran nodel paraneters
Figure 4-22 Krige Variables/Models Screen
The following option sequence selects Cadmium as the variable to
be kriged, enters the variogram model, executes the kriging .
routine, and saves the parameter file:
OPTION
NEW VARIABLE
ACTION
Toggle
-Input
Toggle
Input
Input
Input
Accept
FIELD
Variable
Nugget
Type
Sill value
Major range
Minor range
Angle
VALUE
Cadmium
4.5
Exponential
13.5
300
100
0
QUIT
EXECUTE
QUIT
SAVE PARAM.
Accept
Parameter file Example.kpf
Geo-EAS 1.1
4-20
September, 1988
-------
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 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.
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 Data File Example.grd
"Accept X variable Easting
Accept Y variable Northing
Accept Contour variable *Cadmium
Answer Y
EXECUTE Accept Metafile Metacode.met
Geo-EAS 1.1 4-21 September, 1988
-------
Krigfng estimates produced fronn data file Example.
Contours for «Codmfum
520.
2BO.
240.
20O.
16O.
170.
260. 300. 340. 3BO. 42O. -4-6O. SCO.
Eoating
Figure 4-23
Contours for Cadmium Kriging Estimates
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
Accept
Answer
CONTOUR OPTIONS
NEW LEVELS Accept
Accept
Input
DASH PATTERN Input
Input
Accept
QUIT
EXECUTE
Accept
QUIT
QUIT
X variable Easting
Y variable Northing
Contour variable KSDCadmium
Y
Starting Value
Maximum Value
Cont. Increment
Dash Pattern
Dash Cutoff
# Rep/Label
Metafile
1
3
0.25
1.9
5
Metacode.met
Geo-EAS 1.1
4-22
September, 1988
-------
320.
280.
200.
160.
12O.
Data from Example.grd
Contours for KSDCodmium
26O. 30O. 34O. ABO. +2O. 4-6O. SOO.
Figure 4-24 Contours for Cadmium Kriging Standard Deviations
This map illustrates the reasonable result that the highest
kriging errors are predicted in areas with the lowest density of
sample data.
Geo-EAS 1.1
4-23
September, 1988
-------
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 l - Compare Anisotropic vs. Isotropic varioarams
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).
Step 3. Run Trans with the grid file Compare.grd to create
a new variable called *Cdl-*Cd2. Save the results back
into Compare.grd.
Geo-EAS 1.1 4-24 September, 1988
-------
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 Statl with the grid file Compare.grd to plot
histograms of *Cdl, *Cd2, and *Cdl-*Cd2.
EXERCISE 2. - Compare Point vs. Block kriqinq
Step 1. Run Krige with the data file Compare.grd to create
a grid file of kriged estimates called Compl.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 1.1 4-25 September, 1988
-------
Geo-EAS l.l 4-26 September, 1988
-------
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.—
Geo-EAS 1.1 5-1 September, 1988
-------
5.3
THE MENU HIERARCHY
Dataprep-- Prefix
1
\
1
\
lie* .............
1
\
1
\
_
1
\
n A i A + A ...........
1
\
DOS Command
\ Quit
File Operations - ~
1
\
Column Extract----
1
1
\
1
1
\
Compress----------
1
\
1
\
1
\
1
1
' \
1
1
\ Qui t V
u i rectory
Execute
Qui t
Fi 1 M
i I e
Execute
Quit
Fi le
Execute
Quit
Fz t _ _
lies
Execute
Qui t
Files
Execute
Quit
Fi le
Execute
Qui t
Fj 1 A e
lies
Execute
Qui t
Files
Var i ables
Execute
Qui t
Fi i A «»
lies
Subsetting Condition
Execute
Quit
Fi 1 * e>
lies
Execute
Quit
Fi 1 A e
lies
Execute
Qui t
Fi 1 m c
lies
Execute
Qui t
Fi 1 * e
lies
Variables
Execute
Oui t
F{ i . .
lies
Vari able
Execute
Qui t
\ Out t
Geo-EAS 1.1
5-2
September, 1988
-------
5.4
THE MAIN MENU
D fl T n PREPARATION (l.H)
Data File Prefix :
Scratch File Prefix:
DESCRIPTION:
This option displays file operations along with a
narratiue describing each choice. These operations
are: append, colunnCvariable) extracti row extract,
conpress, ID uar, merge, report and sort.
These operations can produce output files uith a
naxinun of 48 uariables and 18,888 records.
If you uish to use one of these operations or re«juire
nore Information on a specific operation then press
.
Prefix DOS Utilities
Quit
Figure 5-1
Dataprep Main Screen
The Main screen and menu (Figure 5-1) provides options which
allow you to access the DOS Utilities and File Operations menus.
The menu line appears as follows:
Prefix DOS Utilities File Operations Quit
Prefix
The Prefix option is used to enter the prefix strings for the
data file and the scratch file.
DOS Utilities
The DOS Utilities option provides access to the DOS Utilities
menu. The DOS Utilities menu provides access to the DOS commands
such as 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 1.1
5-3
September, 1988
-------
5.5
THE DOS UTILITIES MENU
Data File Prefix : C ^CeoEflSMJatav
Scratch File Prefix:
DOS UTILITIES:
iij|jsi4i!ii4!|
Print
List
Copy
Renane
Delete
DOS Comand
Quit
The directory specified ulll be
displayed. Vou uill be pronpted for
the directory including the prefix ,
it any, Upon execution that
directory ulll be displayed on the
screen. Press
Figure 5-2
Dataprep DOS Utilities Screen
The DOS Utilities screen and menu (Figure 5-2) provides commonly
used DOS commands. These commands operate just as the DOS
commands do. Refer to your DOS manual for further information.
To select an option from the vertical menu, use the 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.
Execute - Selection of this option causes the directory to
be displayed on a new screen. An error message appears if
the directory is non-existent. After the directory is
listed the message "Press to return to menu" is
displayed. The key returns control to the Directory
menu.
Geo-EAS 1.1
5-4
September, 1988
-------
Print
Upon selection of this option the Print menu is displayed.
The Print menu provides the options necessary to print a file.
The Print option is similar to the DOS command "Print".
The menu line appears as follows:
Files Execute Quit
Files - Upon selecting this option, you are prompted for the
name of the file that is to be printed.
Execute - Selection of this option causes the specified file
to be printed. A yes/no prompt appears asking if the printer
is ready. If yes is indicated then the DOS Print command is
executed. When printing begins the Print menu screen is
displayed and a message appears indicating that the file is
being printed.
List
Upon selection of this option the List menu is displayed. The
List menu provides the options necessary to list a file. The
List option is similar to the DOS command "More". The menu line
appears as follows:
File Execute Quit
File - You will be prompted for the name of the file that is
to be listed.
Execute - Upon selection of this option DOS executes 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.
Geo-EAS 1.1 5-5 September, 1988
-------
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 1.1 5-6 September, 1988
-------
5.6
THE FILE OPERATIONS MENU
Data File Prefix : C^GeoEftSMJata^
Scratch File Prefix:
FILE OPTIONS:
Append
Column Extract
Conpress
ID Uariable
flerge
Report
Sort
Quit
Bows of data, le. sanples, are extracted
fron an input file based upon a logical
expression and urltten to an output
file. The first operand is a uariable
and the second operand can be either a
uariable or a constant. The logical
relations are: .LT. , .LE. . .GT.< .GE. ,
.EQ.i.HE..
The data file prefix noted above will
precede the files. Press
Figure 5-3
Dataprep File Operations Screen
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 Geo-EAS input data files called
Demol.dat and Demo2.dat are used to demonstrate each file
operation discussed below.
Demol.dat - ficticious data set 1
3
Easting feet
Northing feet
Arsenic ppm
320.0 311.0 .850
119.0 119.0 .630
115.0 111.0 .560
114.0 269.0 1.020
114.0 269.0 1.020
431.0 137.0 .67
Demo2.dat - ficticious data set 2
3
Easting feet--
Northing feet
Lead ppm
102.0 164.0 .300
122.0 137.0 .360
116.0 119.0 .700
150.0 315.0 .500
148.0 291.0 .710
Geo-EAS 1.1
5-7
September, 1988
-------
Append
Upon selection of this option the Append menu will be displayed.
The Append menu provides the options necessary to append two Geo-
EAS data files. A discussion on the append operation follows in
the Execute option. The menu line appears as follows:
Files Execute Quit
Files - You are prompted for three Geo-EAS data file names.
Upon execution the second 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.
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
4
Easting
Northing
Arsenic
Lead
329-.O
119.0
115.0
114.0
114.0
431.0
102.0
122.0
116.0
150.0
148.0
- ficticious data set 1
feet
feet
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+
.10E+
.10E+
.10E+
.10E+
. . 10E+
.300
.360
.700
.500
.710
Geo-EAS 1.1
5-8
September, 1988
-------
Column Extract
Upon selection of this option the Column Extract menu is
displayed. The Column Extract menu provides the options
necessary to create a Geo-EAS data file with variables extracted
from an input file. The menu line appears as follows:
Files Variables Execute Quit
Files - This option is used to specify two file names. The
first, an input file, is a Geo-EAS data file. The second
file is a Geo-EAS output file.
Variables - This option is used to specify one or more
variables which will be extracted and written 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 want to select another variable. If
yes is indicated then you are prompted for another variable.
If no is indicated then control is returned to the Column
Extract menu.
Execute - Upon selection of this option, the selected
variables 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.
Geo-EAS 1.1 5-9 September, 1988
-------
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 Execute Quit
Files - This option is used to specify two files. The name
of first file entered, an input file, is a Geo-EAS data
file. The name of the second file entered is an output
file.
Subsetting Condition - This option is used to specify a test
condition. The test condition is of the form , where is a variable and
can be a variable or a constant. can
be:
.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.
Geo-EAS 1.1 5-10 September, 1988
-------
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
Demo1.dat - fictitious data set 1
3
E as t i ng feet
Northing feet
Arsenic ppm
119.0 119.0 .630
114.0 269.0 1.02
114.0 269.0 1.02
Each data record in Demol.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.
Geo-EAS 1.1 5-11 September, 1988
-------
Compress
Upon selection of this option the Compress menu is displayed.
The Compress menu provides the options necessary to compress a
Geo-EAS data file. 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 Execute Quit
Files - This option is used to specify two data file names.
The first, an input file, is a Geo-EAS data file. The
second is an output file. After the two files have been
specified, the variable names stored in the input file are
displayed.
Execute - Upon selection of this option, the data from the
input file are stored in a temporary file. Duplicate records
are deleted and the data are 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 feet
Northing feet
Arsenic ppm
320.0 311.0 .850
119.0 119.0 .630
115.0 111.0 .560
114.0 269.0 1.02
431.0 137.0 .670
Note that all duplicate records have been deleted.
Geo-EAS 1.1 5-12 September, 1988
-------
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 file. After the two files have been specified, the
variable names stored in the input file are displayed.
Execute - This option appends a variable called "Sequence #"
to the current listing of variables displayed on the screen.
The variable name "Sequence #" is appended to the variable
names read from the input file. These variable names are
then stored in the 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.
Geo-EAS 1.1 5-13 September, 1988
-------
Merge
Upon selection of this option the Merge menu is displayed. The
Merge menu provides the options necessary to merge two Geo-EAS
data files. The details of this operation are discussed in the
Execute option. The menu line appears as follows:
Files Execute Quit
Files - This option is used to specify the names of two Geo-
EAS data files which are to 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.
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
320.0 311.0 .850 .300
119.0 119.0 .630 .360
115-.0 111.0 .560 .700
114.0 269.0 1.02 .500
114.0 269.0 1.020 .710
431.0 137.00 .6700 1.E31
*** 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.
Geo-EAS 1.1 5-14 September, 1988
-------
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
Demo1.dat - ficticious data set 1
Easting Northing Lead Arsenic
Obs. feet feet ppm ppm
1. 320.0000 311.0000 . .8500000 1.000000
2. 119.0000 119.0000 .6300000 2.000000
3. 115.0000 111.0000 .5600000 3.000000
Geo-EAS 1.1 5-15 September, 1988
-------
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
328-.O 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 l.l 5-16 September, 1988
-------
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 frem 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.
Geo-EAS 1.1 6-1 September, 1988
-------
6.3
THE MENU HIERARCHY
Trans
-Prefix
Read
Title
Create -- Mew Variable ---- Unary Operation
I
Old Variable -/
\ Quit
Delete
Save
\ Quit
-> Unary Operation
> Binary Operation
Binary Operation ->
Indicator Transform ->
\ Quit
Operation -- Constant ---- Execute
I I I
| Variable -/ \ Quit
I
\ Quit
\ Quit
• - Constant
I
Variable •/
Operation -- Constant ---- Execute
I I I
| Variable-/ \Quit
I
\ Quit
\ Quit
\ Qui t
-> Indicator Transform -- Variable - Cutoff
I
| Execute
I
\ Quit
Geo-EAS 1.1
6-2
September, 1988
-------
6.4
THE MAIN MENU
Data File Prefix : C ^GeoEflSVData^
Scratch File Prefix:
Input Flle= Exanple.dat Output File:
Title : Exanple.dat - Geostatistical Enulroimental ftssessnent Software
Operation
Binary
Operand 1 Operator Operand 2
Lead/IB = Lead ' IB. 8
Uariables
Easting northing Arsenic Cadniun Lead
Perforns the aboue operation
Figure 6-1
Trans Main Screen
The Main screen and menu (Figure 6-1) provide the options
necessary to read and save Geo-EAS data files and to create,
delete, or modify variables. The menu line appears as
follows:
Prefix Read Title Create Delete Save Quit
Prefix
The Prefix option is used to enter the prefix for the data file
and scratch file.
Data
The Data option is used to enter the name of a Geo-EAS data file.
Title
The Title option is used to specify a descriptive title for the
output Geo-EAS data file. The title can be up to 66 alphanumeric
characters. No error checking is performed.
Create
The Create option provides access to the Create menu. The Create
menu (described below) is the first in a series of menus that
provide options used to specify a new or existing variable as the
result variable and to perform a specified operation (unary,
binary, transform indicator).
Geo-EAS 1.1
6-3
September, 1988
-------
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 are
entered then an error message is displayed. If the output file
already exists then a Yes/No prompt will appear asking if the
file should be overwritten. The data in the temporary file is
copied to the output Geo-EAS data file. If an error should occur
while opening the output file then an error message is displayed.
While the file is being saved the message "Writing data..."
appears. After the data has successfully been written a message
is displayed (press any key to continue).
6.5 THE CREATE MENU
The Create menu provides the options necessary to perform
transformations to a Geo-EAS data file. The menu line appears as
follows:
New Variable Old Variable Quit
New Variable
When the New Variable option is selected a new variable is
created in the scratch file. The new variable takes on values
generated from the specified operation (unary, binary, 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
Geo-EAS 1.1 6-4 September, 1988
-------
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.
The Unary Operation menu provides an option to select a
unary operation. The menu line appears as follows:
Operat ions Quit
Geo-EAS 1.1 6-5 September, 1988
-------
Operation - This option is used to specify the unary
operator. You are prompted for a unary operator from the
toggle field. Upon making the selection, control is passed
to the Unary operand menu (described below).
The Unary Operand menu provides the option to select an
operand for the unary operation. The menu line appears
as follows:
Constant Variable Quit
Constant - This option is used to assign a constant
value to the unary operand. You are are prompted for
the constant value. The constant value is entered into
a numeric(floating point) field. The default value is
initially zero. If the value entered results in a
numeric overflow then a message is displayed. Upon
pressing any key, control is returned to the Unary
Operand menu. If the constant value entered is
acceptable then control is passed to the Execute
menu (described below).
Variable - This option is used to select an existing
variable for use as the unary operand from a toggle
field. Upon making the selection, control is passed to
the Execute menu (described below).
The Execute menu provides the option necessary to
initiate any unary operation. The menu line
appears as follows:
Execute Quit
Execute - This option is used to initiate the
unary operation. During processing the message
"Processing data..." is displayed on the screen.
After processing is complete the 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
Geo-EAS 1.1 6-6 September, 1988
-------
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.
The Binary Operand One menu provides the options to select
operandl for the binary operation. The menu line appears as
follows:
Constant Variable Quit
Geo-EAS 1.1 6-7 September, 1988
-------
Constant - 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.
Variable - 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
Operation - This option is used to specify the binary
operator. You are prompted for a binary operator from
a toggle field. Upon making the selection control is
passed to the Binary Operand Two menu (described
below).
The Binary Operand Two menu provides the options to
select operand2 for the binary operation. The menu
line appears as follows:
Constant Variable Quit
Constant - This option is used to specify a
constant for the binary operand two. This option
is similar to the binary operand one constant
option described previously in the Binary Operand
One menu. The exceptions are that the wording
refers to operand two and not operand one, and
upon entering an acceptable value, control is
passed to the. Execute menu (described below).
Variable - This option is used to specify an
existing variable for binary operand two. It is
similar to the binary operand one variable option
described previously in the Binary Operand One
menu. The exceptions are that the wording refers
to operand two and not operand one, and upon
making a selection, control is passed to the
Execute menu (described below).
Geo-EAS 1.1 6-8 September, 1988
-------
The Execute menu provides the option needed
to initiate the binary operation. The menu
line appears as follows:
Execute Quit
Execute - This option initiates the binary
operation. During processing the message
"Processing data..." is displayed on the
screen. The Execute(binary) option causes
the same prompts as in the Execute option of
the unary operation. Refer to the Execute
option of the Execute 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).
Indicator Transform
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 the
threshold value. The Indicator Transform option provides access
to the Indicator Transform menu.
The Indicator Transform menu provides the options to select
the operands and to execute the operation. The menu line
appears as follows:
Variable Execute Quit
Variable - This option is used to specify two operands. The
first operand is an existing variable and the second operand
is the threshold value which is a constant. The message
"Select variable for operation (use 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 1.1 6-9 September, 1988
-------
7.4
THE MAIN MENU
A program to conpute uniuariate descriptiue statistics
File Prefix: C : VGeoEASNDataX
File
Data File Nane : Exanple.dat
Uariable
Variable : Cadnlu*
Ueight : Nona
Log Option : Off
Li. its
Minimi* : .888
Maximm : 16.788
S Variable* 5
• Data records 68
« Hissing Data 8 (2
Execute
lisa this option to conpu
display the statistics.
of additional graphs and
-ill be displayed.
Ob»<=8)
te and
A menu
options
Prefix Data Uariable Limits
Compute basic descriptive stats.
Batch Statistics Quit
Figure 7-1
Statl Main Screen
The main menu and screen (Figure 7-1) has options to allow
specification of the data file names, the selection of the
variable to be used, the selection of upper and lower limits for
the variable, calculation of statistics (univariate), and
generation of a batch statistics report. The menu 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
Geo-EAS 1.1
7-2
September, 1988
-------
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 is 1).
Log Option - A two valued toggle (On/Off) field to enable or
disable the Log option. If the Log option is enabled and a
weighting factor variable selected then the statistics are
calculated for the Weight value multiplied by the (natural
log of the Variable value). Whenever the Log option is
enabled sample values less than or equal to zero are
counted but not used in the computation. The default value
is "Off".
Limits
The Limits option allows computation of statistics for a subset
of the data which lie between the specified minimum and maximum
sample values. You may specify the upper and lower limits placed
on the values used for computing the basic statistics.
Minimum - A numeric field which contains the lower limit on the
sample values used in the computation. The default value is
the minimum value of the selected variable.
Maximum - A numeric field which contains the upper limit on the
sample values used in the computation. The default value is
the maximum value of the selected variable.
Execute
The Execute option provides access to the Results screen and
menu. When the Log option 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 1.1 7-3 September, 1988
-------
7.5
THE RESULTS MENU
Data File : G:
UMiK
^GeoEASNDataVExanp le
imm ^
.dat
Uarlable : Cadniun
Lower Unit :
Upper Linlt :
1 Obseruatlons
1 Missing Data
1 Retained
Rean
Uar lance
Std. Oeulation
xCoef. Uarlatlon
Skewness
Kurtosis
.888
16.788
60
0
60
7.8858
15.5315
3.9410
49.9889
-.1510
2.4639
Sun of Heights
ninlnun Oalue
25 th Percent lie
Hedlan
75th Percent lie
naxinun Ualue
60.0080
tOOOO
5.3088
7.6888
18.8888
16.7880
Probability Plot Exanlne Quit
Choose histogran paraneters / display graph
Figure 7-2
TStatl Results Screen
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 "Examine
Data"), and to display the Histogram screen and menu. The
Results Screen displays univariate statistics for the selected
variable. The menu line appears as follows:
Histogram Probability Plot Examine Quit
Histogram
The Histogram option provides access to the Histogram screen and
menu. First a 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.
Geo-EAS l.l
7-4
September, 1988
-------
No*M*l Probability Plot for CadntuM
Data file: Cxanplv.dat
1 •
y a.
4++'
V
1 18
CUMU
s
>
^
*
/
/**
+ **
f
38 38 70 99 99
lattw* P»po>nt
Statistics
N Total 68
N Hiss a
N Used 88
ttean 7.885
Variance 15.531
Std. Dew 3.941
* C.V. 49.981
. Skewness -.151
Kurtosis 2.464
* nininun .888
25th * 5.388
T1 tied Ian 7.G88
75th * 18.888
tlaxinun 16.788
Figure 7-3
Statl Probability Plot
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 the interquartile range, and the "X"
marks the arithmetic mean. The endpoints of the outward
extending lines depict the minimum and the maximum values.
Components of a BOXPLOT
1 st Quartile
Minimum
I
Median
Mean
i
3rd Quartile
X
Maximum
1
10
T
Scale
20 30
40
50 60
70
80
90
Figure 7-4
The Components of a Boxplot
Geo-EAS 1.1
7-5
September, 1988
-------
Examine
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.
Rank
1
2
3
4
5
6
7
8
9
IB
11
12
13
14
15
16
Data Ualue Weight Cun. x
.8888
.8888
.9888
1.2888
1.2888
1.6888
1.7888
3.2888
3.4888
3.8888
3.9888
4.8888
4.4888
5.2888
5.3888
5.5888
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
1.8988
-1.8988
1.8988
1.8988
1.8988
.888
.825
.842
.858
.875
.892
.188
.125
.142
.158
.175
.192
.288
.225
.242
.258
P rob It
-2.394
-1.968
-1.732
-1.569
-1.448
-1.331
-1.236
-1.158
-1.873
-1.881
-.935
-.872
-.812
-.755
-.781
-.648
Redlo
38
28
29
34
32
45
33
31
47
39
11
22
43
9
24
21
F^6 or
i to scroll : <1> thru
<9> to position
tMSim
uit
^Mi
Figure 7-5
Statl Examine Screen
7.6
THE HISTOGRAM OPTIONS MENU
Data File : C^GeoEAS^DataVExanple.dat
Uariable : Cadniun
Lower Linit : .888
Upper Unit : 16.788
Type : Absolute
Class Units
nininun .888
Class Width 1.888
1 Classes 28
Axes
X Axis V Axis
Hlninun = .888 .888
Haxinun : 28.888 9.758
Tic Spacing : 4.888 3.888
Rain Title Histogran
Sub Title Data file: Exanple.dat
X Axis Cadniun (ppn)
V Axis Frequency
Type Class Units Axes Titles Results J1BHMHJ1UII Quit
Uleu the hlstogran as a graph
Figure 7-6
Statl Histogram Options Screen
Geo-EAS 1.1
7-6
September, 1988
-------
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 1.1 7-7 September, 1988
-------
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.BAR 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 - An alphanumeric field which may contain up to 60
characters for the X axis. 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 - An alphanumeric field which may contain up to 60
characters for the Y axis. The default label is
"Frequency".
Results
The Results option allows:access to the Histogram Results screen
and menu (Figure 7-7). This screen displays the histogram
results. The results are in tabular form. The display
may be scrolled as in the Examine option (described above).
View Graph
The View Graph option allows access to a screen that displays the
histogram (Figure 7-8). The resulting histogram is accompanied
by a box plot (described in the Probability Plot Option of the
Results menu), and some univariate statistics.
Geo-EAS 1.1 7-8 September, 1988
-------
Data File : C^GeoEAS^Data^Exanple.dat
Uar table : Cadniun
Lower Llnit : .088 Class flln. •'
Upper Llnit :
«=)
1
2
3
4
5
6
7
8
9
IB
Upper Llnit
1.888
2.888
,
4.888
5.888
O •DDO
7.888
8.888
9.888
18.888
16.788 Class Uldth : 1
Fres.
3
4
.
5
1
5
8
4
5
4
Sun Weights Bel
3.888
4.888
* • •
5.888
1.888
5.888
8.888
4.888
5.888
4.888
F.
858
867
883
817
883
133
867
883
867
flax. Ualue
.988
1.788
.
4.888
4.488
5.888
7.888
7.688
9.888
18.888
.888
.888
Class Mean
.388
1.425
3.668
4.488
5.588
6.658
7.275
8.688
9.825
!jUse
T or * Jieys to Scro 1 1 ,
or to CJuitB
Figure 7-7
Statl Histogram Results Screen
HistogrraM
Data ftl«: ExiMplv.dat
».
6.
b
3. •
—™
— 1
^
™~
_
1
0. 4. >. 12.
Cadnlun
__
Statistics
1 N Total 68
n
H nis* a
N Used 68
Mean 7.885
Variance 15.531
Std. Daw 3.941
% C.V. 49.381
Skenness -.151
Kurtosis 2.464
nininun .888
25th X 5.388
Median 7.688
75th X 18.888
Haxinun 16.788
1C. 30.
Figure 7-8
Statl Histogram
Geo-EAS 1.1
7-9
September, 1988
-------
Geo-EAS l.l 7-10 September, 1988
-------
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 10000 samples. If the data file contains
more than 10000 samples, only 10000 will be used by Scatter.
8.3 THE MENU HIERARCHY
Scatter Prefix
Data
Variables
Options
Execute
\ Quit
8.4 . THE MAIN MENU
The Main menu and screen (Figure 8-1) has the options to allow
specification of the data 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.
Geo-EAS 1.1 8-1 September, 1988
-------
•J'i •••••IB li
ft progran for producing scatter plots
File Prefix: c:^GeoEASM)ata>>
Data File: Exanple.dat
Variables
X Uarlable : CadniiM Log : 'Off
V Variable : Lead Log : Off
Options
Regression : Ves
Equal Scaling : fto
I Data records : 60
1 Hissing data • 9
Execute
Use this option to create the
plot •
Prefix Data Variables Options
Generate the plot
Quit
Figure 8-1 Scatter Main Screen
Data
The Data option is used to enter the name of a Geo-Eas data file;
Variables
The Variables option allows the selection of variables that are
to be used as the X and Y coordinate values, and the sample
values to post. The choices available are the variable names as
specified in the data file. The screen fields accessed from this
option are:
X Variable - A toggle field for selecting the variable name whose
values will be used as the X-coordinates. The default X
Variable is the first variable in the data file.
Y Variable - A toggle field for selecting the variable name whose
values will be used as the Y-coordinates. The default Y
Variable is the second variable in the data file.
Log - Two two-valued toggle fields to enable or disable a
logarithmic-transformation of 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"
Geo-EAS 1.1
8-2
September, 1988
-------
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 R Squared value (a
measure of correlation) are displayed to the right of the
graph. The default value for Regression is "Yes".
Equal Scaling - A two-valued (Yes/No) toggle field to enable or
disable the use of 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.
Scatter Plot
488.
38O. •
* 28O.
100.
. O. •
O
fpon data fll» Cxanplv.dat
' 4
L^&T^
Regression Results:
* Pairs : 68
Slope : 6.678
Intercept : -3.649
Correl. coeff.: .462
4. •. 12. It. 2O.
Cadniun
Figure 8-2
Scatter Plot
Geo-EAS 1.1
8-3
September, 1988
-------
Geo-EAS 1.1 8-4 September, 1988
-------
SECTION 9
PREVAR
9.1 WHAT PREVAR DOES
Prevar is a preprocessor program for the program Vario. All
variogram calculations use the distance and relative direction
between pairs of points in the sampled area. Prevar computes
these so that variogram parameters may be changed and variograms
recalculated more quickly in Vario. The output from Prevar is a
"pair comparison file" (PCF). " The pair comparison file contains
the input data file contents along with distances and relative
directions between pairs of sample points. This information is
used by the 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. If is recommended that some limits on the distance between
points be specified.
9.2 DATA LIMITS
Due to the storage requirements of Vario, Prevar must impose
limits on the number of sample points in the input file and on
the number of pairs for which distances and directions 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 limits were imposed (N2+N)/2 inter-pair distances and
directions would be computed. A file with several hundred
samples^ would easily generate too many pairs for Vario. The
Limits option is used to restrict the number of pairs computed.
Prevar will compute a maximum of 16384 pairs.
9.3 THE MENU HIERARCHY
Prevar Prefix
Files
Variables
Limits
Execute
\ Quit
Geo-EAS 1.1 9-1 September, 1988
-------
9.4
THE MAIN MENU
ft preprocessor for program UflRIO
File Prefix^ C:xCeoEftS^Data>«
Files
Data File: Exanple.dat
Pair Conparison File: Exanple. pef
Uar tables
X Uarlable: Easting
V Uarlable: Northing
Limits
flininun Flax i mum
X: 254.488 492.888
y: 118.888 315.888
Distance1 .888 388.647
Uarlables S
Records 68
Pairs possible 1778 «ax= 16384
Execute
Select this option to build the
pair comparison file. Distances
and directions for all pairs uill
be computed (subject to limits),
sorted by distances, and sawed.
Prefix Files Variables Units [
Build the pair comparison file
Quit
Figure 9-1
Prevar Main Screen
The Main screen and (Figure 9-1) menu has the options to allow
specification of the input data and the pair comparison file
names, the selection of the variables to be used and the limits
on sample coordinates and the interpair distances. The menu line
appears as follows:
Prefix Files Variables Limits Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Files
The Files option is used to enter the input data and the pair
comparison file names. The screen fields accessed from this
option are:
Data File - An alphanumeric field that may be up to 14 characters
used for entering the name of a Geo-EAS data file.
Pair Comparison File - An alphanumeric 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
Geo-EAS 1.1
9-2
September, 1988
-------
prompt provides alternatives to continue or quit from the
option.
Variable
The Variable option allows the selection of the variables that
are to be used for the X and Y coordinate values. The choices
are determined by the variable names in the input data file.
The screen fields accessed from this option are:
X Variable - A toggle field used for selecting the variable name
whose values will be used as the X coordinates. The default
X variable is the first variable in the data file.
Y Variable - A toggle field used for selecting the variable name
whose values will be used as the Y coordinates. The default
Y variable is the second variable in the data file.
Limits
The Limits option is used to restrict the area and interpair
distance for pairs retained in" the pair comparison file. The
screen field accessed from this option are:
Minimum - Three numeric fields for entering the minimum X and Y
coordinate values and the minimum distance between pairs.
The default values displayed are determined from the
coordinate variables in the data file.
Maximum - Three numeric fields for entering the maximum X and Y
coordinate values and the maximum distance between pairs.
The default values displayed are determined from the
coordinate variables in the data file.
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 1.1 9-3 September, 1988
-------
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.
Geo-EAS 1.1 10-1 September, 1988
-------
10.3
THE MENU HIERARCHY
V a r i o
Prefix
Data
Variable
Limits
Options/Execute -
0 i r ec t i on
New Lags
Change Lags
Post Plot
Execute --•
\ Quit
10.4
\ Quit
THE MAIN MENU
Type
Plot
BoxPlot
Lag Results
Model
\ Quit
H i stogram
Scatter Plot
Examine
Write
Quit
Model
Plot
Options -- Titles
| Tic Spacing
| Limits
\Quit
Quit
ft progran for confuting uariograns
File Prefix :C:VteoEASNDataN
File
Pair Conparison File' Exanple.pcf
variable
Uariable: Cadnlun
Log Option: Off
Units
•nininun: .880
, • rtaxinun: 16.788
Uars : 5 I Kept
Data = 68 • Obs<=8
Pairs: 1778 9 Hissing
UarlograH Options
Use this option to dlspla
UarlograH Options Screen
Uariogran options nay be
and the uariogran nay be
: 68
: 2
: 8
y the
and nenu.
selected
computed.
Prefix Data Uariable Lin Its JJBllllMJiWIIBffB Quit
Specify uariogran optIons• conpute
Figure 10-1 Vario Main Screen
Geo-EAS 1.1
10-2
September, 1988
-------
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 tire 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.
Geo-EAS l.l 10-3 September, 1988
-------
Options/Execute
The Options/Execute option provides access to the Options screen
and menu (Figure 10-2), described below.
10.5
THE OPTIONS MENU
1 1*19
Uarlable :Cadnlun
ninlnun : .888
naxinun : 16.7
Lag
1
Direction : .098 2
Tolerance : 90.888 3
Hax Banduldth: HflX 4
5
7
Lag Spacing 8
9
Hininun : .888 18
Haxinun : 158.888 11
Increnent '• 15.888 12
••il.'Kl
Pair File
flln. Distance
tlax. Distance
Distance Lag
15.888 13
38.888 14
45.888 15
60 • BOO 16
75.888 17
98.888 18
185.888 19
128.888 28
135.888 21
158.888 22
23
24
• Exanple.pcf
: 6.88
: 382.
Distance
Direction fleu Lags Change Lags Post Plot iHV»JillMH Quit
Conpute results - display graphics and node 11 ing nenu
Figure 10-2 Vario Options Screen
The Options screen and menu (Figure 10-2) provides a means to
specify variogram options, view a post plot of the data and
compute the variogram results. The menu line appears as follows:
Direction New Lags Change Lags Post Plot Execute Quit
Direction
The Direction option allows you to specify the pair orientation
(selection) criteria. Figure 10-3 illustrates how these
parameters affect the grouping of pairs within a lag interval.
The screen fields accessed from this option are:
Direction - A* numeric field for entering the pair direction in
trigonometric degrees. Acceptable values range from 0 to
180 degrees (excluding 180). The default is zero degrees,
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.
Geo-EAS 1.1
10-4
September, 1988
-------
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.
An illustration of the
(unction of the Lag Cutoff,
Direction, Tolerance,
and Maximum Bandwidth
parameters.
The pair P1,P7 will be
included in the computation
for Lag 1. The pairs P1,P2
and P1,P6 will be included
in the computation for Lag2.
P1
2nd Lag
Cutoff
Ma»mum
Bandwidth
P4
1st Lag
Cutoff
Direction
Angle
X axis direction
Figure 10-3
An Illustration of the Direction Parameters
New Lags
The New Lags option allows you to choose new pair distance
intervals. Pairs are included in a lag if the distance for the
pair is greater than the previous cutoff value and less than the
cutoff value for that lag. The screen fields accessed from this
option are:
Minimum - A numeric field for entering the minimum inter-pair
distance. The first lag 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 = ^one- half the maximum interpair distance, and Increment
= Maximum divided by 10.0. These values may not be appropriate
for the data configuration. Once these parameters are specified,
the lag cutoff distances are displayed in columns on the Options
screen.
Geo-EAS 1.1
10-5
September, 1988
-------
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 data.
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.
320.
28B.
Plot of *mpl* -locations
zee.
169.
128.
80.
240.
32B.
400.
Eastinsr
480.
360.
Figure 10-4 Vario Post Plot
Execute
When the Execute option is selected the program displays the
Results-screen and computes the lag -results before providing
access to the Results screen and menu (Figure 10-5). This menu
is described below.
Geo-EAS 1.1
10-6
September, 1988
-------
10.6
THE RESULTS MENU
Uarlable:
ninlnun :
Maxinun :
Pairs
1 17
2 65
3 97
4 111
5 141
6 194
7 198
8 165
9 147
18 115
11
12
Cadnlun
.888
16.788
ftug Distance
11.996
23.837
38.114
52.658
67.338
82.717
97.658
111.726
127.411
141.538
1 •!•»«••«• 1 n
Direction : .888
Estinator : Uariogran Tolerance : 98.888
Total Pairs = 1242 Bandwidth : n/a
Estinate
7.818
8,838
11.3%
12.998
13.388
15.834
15.842
16.182
16.468
15.6%
Pairs Aug Distance Estinate
13
14
15
16
17
18
19
28
21
22
23
24
Type JUrai Box Plot Lag Results node! Quit -
Plot the selected estlnator us. average distance
Figure 10-5 Vario Results Screen
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 "Non-Ergodic" . The default is
"Variogram". See the glossary for a definition of these terms.
Plot
The Plot option allows you to view a variogram plot of the
selected estimator. .The distance (h) is plotted along the
horizontal axis, and the variogram is plotted on the vertical
axis. The type of estimator and the variable name are displayed
as the graph title. Vertical and horizontal axes scaling and the
tick mark spacing are calculated by the program. Displayed on
the right side of the graph are the number of pairs, the lag
minimum and maximum, the direction, tolerance and maximum
bandwidth, the sample limits, and the mean and variance of the
sample values. An example graph is displayed in Figure 10-12 near
the Plot option in the Modeling screen.
Geo-EAS l.l
10-7
September, 1988
-------
Box Plot
The Box Plot option allows you to view a variogram boxplqt,
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 -quartlie, and
the top is the third quartile. Therefore, 50% of the data falls
within the range represented by the rectangle. The mean is
represented by "x" and the median is represented by the
horizontal line through the rectangle. The distance (h) is
plotted along the horizontal axis, and the difference squared is
plotted on the vertical axis. The variable name is displayed in
the title of the graph. Vertical and horizontal axes scaling and
the tick mark spacing are calculated by the program. Displayed
on the right side of the graph is the number of pairs, the lag
minimum and maximum, the direction, tolerance and max bandwidth,
the variable minimum and maximum, and the mean and variance of
the data.
Boxplot top CadniuM
JIMP. '
2S0. •
£
J 200. •
9
*
• 1S0 •
o •<•.
e
£
% 1 ftft
^ **•
o
30. •
0. •
[
5 F
i E
^IP
E
File :Exanple.pcf
Pairs : 1242
Direct.: .888
Tol. : 98.888
MaxBand : n/a
Cadniun Linlis
Hintnun: .888
ftaxinun: 16.788
flean : 7. BBS
Var. : IS. 531
0. 40. 80. 120. 160.
Oictano*
Figure 10-6 Vario Box Plot
Lag Results
When Lag Results option is selected you will be prompted to
select a lag number before access is provided to the Lag Results
screen and menu. This is accomplished by using the 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.
See the section on the Modeling menu below for more information.
Geo-EAS 1.1
10-8
September, 1988
-------
10.7
THE LAG RESULTS MENU
IM
Lag Munber : 6
Hunter of Pairs = 194
All data
Hean : 7.885
Uariance : 15.531
Max Distance (LE)
Auerage Distance
Lag data Fran (pairs)
8.286 8.239
* 14.8% 13.319
Spatial correlation estimators
Uarlogran IS
Relative Uario.
tladogran 2
fton-Ergodic Uario. 17
.834
.231
.219
.383
Statistics for
nininuit
2Sth x-tlle
ttedian
Hean
TSth x-tile
Maxinun
: 75.888
: 98.888
: 82.717
To (pairs)
8.334
14.942
difference^
.888
1.698
16.888
31.668
43.568
249.648
Scatter Exanine Urlte Quit
Generate a Lag-Histogran
Figure 10-7 Vario Lag Results Screen
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 are 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
are plotted for all pairs in the lag, subject to the limits
criteria (direction, tolerance, bandwidth, sample value limits
and interpair distance) which have been specified. Displayed on
Geo-EAS 1.1
10-9
September, 1988
-------
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 the sample value
limits. Figure 10-9 displays an example lag-scattergram.
120.
100.
80. •
31
u
c
»
3 60.
9
t
ti
In
40. •
20. •
0
rr
.
__^
LJ
eg
<
a Hl«to0r*n for Cadolun
-n
1. 160. 240. 32
Z? Squ»M4
Lag » 6
Pairs 194
Vario. 15.834
HinDlst 75.888
HaxDIst 98.888
Direct. .888
Tol. 98.888
HaxBand n/a
Cadniun Lin its
tlininun .888
MJ.W i M M 1 R *7PM
flOX iniWI ID . /IXJ
B.
Figure 10-8 Vario Lag-Histogram
Lav Scatter Plot foi> CadnluM
2O.
16.
12. •
8.
4.
P a r t
Lag « :
Pairs :
Vario. :
ninDist:
HaxDIst:
6
194
15.834
75.888
98.888
Direct.: .888
Tol. : 98.888
HaxBand: n/a
Cadniun Linita
tlininun: .888
tlaxinun: 16.788
0.
4. •. 12
1st rein* In
16.
20.
Figure 10-9 Vario Lag-Scattergram
Examine
The Examine provides access to the Examine Lag Results screen,
displayed in Figure 10-10. The Examine Results screen displays
in a tabular form a pair index number, the first and second
values, the distance, the direction, and the difference squared
for each pair in the lag. These are sorted in order of difference
squared. You can use the arrow keys or the <1> to <9> keys to
Geo-EAS 1.1
10-10
September, 1988
-------
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.
Pair
43:
S6:
48:
52:
32:
57:
46:
58:
29:
55:
36:
5?:
58:
58:
5?:
57:
27
29
28
34
6
17
43
29
25
29
28
22
33
32
45
29
ft
1st Value
4.488
11.888
18.488
11.688
1.288
16.788
15.888
11.688
.988
11.888
11.688
16.788
14.988
14.988
16.788
16.788
^m-.-m.mmim*
2nd Ualue
14.508
.988
.888
1.288
11.688
6.188
4.488
.988
11.688
.988
.888
4.888
1.788
1.288
1.688
.988
Distance
82.428
78.388
78.954
89.885
88.936
78.359
76.859
83.896
88.522
88.638
79.818
79.986
83.888
88.888
84.521
76.348
a
Direction
234.382
284.178
223.152
72.746
74.521
287.358
58.878
246.158
83.774
388.964
285.866
81.363
98.888
278.888
388.668
264.588
Difference^
182.818
182.818
188.168
188.168
188.168
112.368
112.368
114.498
114.498
118.818
134.568
161.298
174.248
187.698
228.818
249.648
isa
" or
* to scroll
<1> thru <9> to position
or OPuitM
Write
Figure 10-10 Vario Examine Lag Results Screen
The Write option allows you to save the lag results in a Geo-EAS
data file. The Variable, From , To Distance, Direction,
Difference and Difference"2 will saved in a file. The file name
is entered on the message line, when the Write option is selected.
The default file name is "LagResult.dat". If the file already
exists, a Yes/No prompt provides an alternative to quit or
proceed. The lag results file may be used with 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
Geo-EAS 1.1
10-11
September, 1988
-------
Pairs flujr Distance
1
2
3
4
5
f>
7
g
9
18
11
12
13
14
15
16
17
17
65
97
111
141
194
198
ICC
1O*J
147
115
11.996
23.837
38.114
52.658
67.338
82.717
97.658
m72fc
• % €JO
127.411
141.538
|jl!|
Ualue
7.818
8.838
11.396
12.998
13.388
15.834
15.842
tfc 1H2
XD • XOb
16.468
15.696
EU
Pairs flug Distance
18
19
28
21
22
23
24
node!
Nugget '•
Type Sill
Spherical 11.888
Ualue
5.888
Range
188.888
ttodel ilinn Options Quit
Plot the uariogran and Model
Figure 10-11 Variogram Modeling Screen
Model
The Model option allows you to edit or enter the parameters for
the variogram model. Up to four nested variogram structures and
a "nugget" component can be included in the model. The screen
fields access from this option are:
Nugget - A numeric field for entering the nugget effect.
value entered must be greater than or equal to 0.
The
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.
Geo-EAS 1.1
10-12
September, 1988
-------
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. Press to clear the screen and access the
Variogram Modeling menu.
«.,*.,..- ,0, <**,,_
Par
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8
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File :
Pairs :
Direct.:
Tol. :
HaxBand:
Cadnlun
tllninun:
tlaxinun:
Heart :
Uj...
a. 4B. aa. 120. lee.
Distance
Exanple.pcf
1242
.888
MB0A
• KwO
rVa
Llnits
.888
16.788
7.885
15.S31
Figure 10-12 Plot of Variogram with Model Curve
Options
The Options option provides access to the Graph Options screen
and menu, displayed in Figure 10-13.
10.9
THE GRAPH 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 1.1
10-13
September, 1988
-------
Titles
(lain Title : Uariogran for Cadnlun
Subtitle :
X Label = Distance
V Label : Uariogran
Tlcknark Spacing
X Tlcknark Spacing : 18.888
V Tlcknark Spacing : 3. 888
Linits
X Axis ttininuH : .888
X Axis rtaxlnun : 168.888
V Axis lUninun : .888
V Axis HaxinuH : 19.588
Titles Tic Spacing Linits Quit
Plot the graph and nodel cur we
Figure 10-13 Variogram Graph Options Screen
Titles
The Titles option allows you to enter the title and labels for
the graph. The screen fields accessed from this option are:
Title - An alphanumeric field which may contain up to 60
characters each, for the title on the graph. The default
title contains the type of estimator and the variable name.
Subtitle - An alphanumeric field which may contain up to 60
characters for the graph subtitle.
X Label - An alphanumeric field which may contain up to 60
characters for the X axis label. The default label
is "Distance".
Y Label - An alphanumeric field which may contain up to 60
characters for the Y axis label. The default label
is the type of estimator selected.
Tic Spacing
The Tic Spacing option allows the specification of the spacing of
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.
Geo-EAS 1.1
10-14
September, 1988
-------
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 - A numeric field for entering the minimum
coordinate value to be used on the Y axis. The default
value is zero.
Y Axis Maximum - 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 1.1
10-15
September, 1988
-------
Geo-EAS 1.1 10-16 September, 1988
-------
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-EAS
data file for further analysis.
11.2
DATA LIMITS
Xvalid requires that the input data file contains at least 3
but no more than 48 variables. Two of these variables must
represent the coordinates of sample locations. No more than 1000
samples may reside in the data file. If more than this number
are encountered, only the first 1000 values will be used for
cross-validation.
11.3 THE MENU HIERARCHY
Xvalid Prefix
Data
Variables
Options/Execute Type
\ Quit
Search
Model
Execute
Debug
\ Quit
- Error Map
Scatter Plot
Histogram
Write
Examine
\ Quit
Geo-EAS 1.1
11-1
September, 1988
-------
11.4
THE MAIN MENU
X U n L I D (1.0)
A progran for crass-validating krlglng parameters
File Prefix:
File
Data File Mane : Exanple.dat
I Variables = 5
• Data points • 68
I Missing data = 8
(2 Obs<=8)
Uartables
X coordinate
V coordinate
Uariable to krige
Log option
Easting
Northing
Cadniun
Off
Opt1onsxExecute
Use this option to specify the
XUALID krlglng options screen•
This screen will be presented only
if a file and variables have been
chosen• Once options have been
selectedi kriging nay begin.
Prefix Data Variables
XUALID options screen
Quit
Figure 11-1 - Xvalid Main Screen
The Main screen and menu for Xvalid, shown in Figure 11-1,
provides options to specify the file prefix, the input data file
and variables, and to access the Options/Execute menu. The menu
line appears as follows:
Prefix Data Variables Options/Execute Quit
Prefix
The Prefix option is used to enter the prefix for the data file
name.
Data
The Data option is used to specify the name of the Geo-EAS data
file to be used 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.
Geo-EAS 1.1
11-2
September, 1988
-------
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 (OYi/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:NGeoEASVDataNExanpIe.dat
X Uariable: Easting
V Uariable: Northing
Kriging : Cadniun
Log option: Off
Kriging Type: Ordinary
Search
R Hajoi
R Hlnoi
Angle
nin Di<
Uarlogran Model
Nugget :
Type Sill
1 Spherical 11.888
2
3
4
Ellipse Paraneters
r : 88.888
r : 88.888
: .888
st: .888
Distance type :
Nun. sectors •'
Max pts'sector:
Hln pts to use:
Enpty sectors :
Euclidean
1
8
1
8
S.888 Global Mean:
Major Range Minor Range Ellipse Angle
188.888 188.888 .888
v
Type Search Model
Debug Quit
Begin kriging the sanple values
Figure 11-2 Xvalid Options Screen
The Options screen and menu, shown in Figure 11-2, has the
options to specify the parameters to be used for kriging, and to
initiate they 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
Geo-EAS 1.1
11-3
September, 1988
-------
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 - 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.
Search ellipse and Variogram anisotropy ellipse
Parameters
X coordinate axis
Figure 11-3 Search (and Variogram) Ellipse Parameters
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.
Geo-EAS 1.1
11-4
September, 1988
-------
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 Pts/Sector (Maximum points per
sector) criterion is exceeded in a given sector. If this
should occur, only the "closest11 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.
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.
Geo-EAS 1.1 11-5 September, 1988
-------
Model
The Model option allows specification of the variogram model to
use when kriging. Screen fields are provided for a nugget effect
value and up to four nested variogram structures. Each structure
is specified with a structure type, a sill value, and an ellipse
of influence. If simple kriging 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 - 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 nested
variogram structures:
Type - a toggle field for indicating the type of the structure.
The toggle field choices for type are " " (none),
"Spherical", "Gaussian", "Exponential", "Linear". The
default type for all four structures is "none". If a
structure is entered and the type is subsequently changed to
"none" the structure will be deleted from the variogram
model. The order of the variogram structures on the screen
is unimportant; neither do they need to be in a contiguous
order on the screen.
Sill - a.numeric field for. entering the sill value for a
variogram structure. A non-zero, non-negative value is
required here. In a linear variogram structure the "sill"
must be chosen so that the corresponding "range" parameter
value(s) will result in the desired slope(s); the actual
model continues to increase indefinitely with distance.
Major Range - a numeric value for entering the longest range of
influence of the variogram structure. The Major Range must
be non-zero, and non-negative. This may be thought of as
similar to the R Major parameter described in the Search
Geo-EAS 1.1 11-6 September, 1988
-------
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).
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.
Geo-EAS 1.1 11-7 September, 1988
-------
XUALID (Cross validation)
320.
280. •
» 240.
e
f 200. •
C.
0
z 160. •
120. •
80. •
f ^ » , a
* X • '
* x ,
X ° ° >
* _ »
0 • > 4
0 o i
0 'o a
0 i i
4 0
X o * ,
0 4
X ' «
4
CadMiuM
•f < 5.300
X < 7.600
0 < 10.800
X\*ia ooa
>— 10. DIM
0 - Missing
240. 329. 400. 480. 960.
Easting
It X V 2 2» KsDev
18 278. 119. 7.28 3.33 3.41
N
7
Figure 11-4 Xvalid Kriging Display
Debug
The Debug option is provided on the menu as a means of
identifying the keys used for enabling or disabling the Debug
displays. This option does not actually do anything, but moving
the cursor bar to this menu option will display the Debug display
names, and the corresponding < -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 the 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 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.
Geo-EAS 1.1
11-8
September, 1988
-------
11.6
THE RESULTS MENU
Data File
X Uarlable
V Variable
Krig Ing
Type
ninlnun
25th /tile
fed Ian
75th xtlle
Maxlnun
H
Hean
Std. Dew.
• C^CeoEftSMJa taVExanple.dat
: Easting
: Northing
•' Cadnlun
: Ordinary
Uariable
.888
5.388
7.688
18.888
16.788
68
7.885
3.941
a
8
Estlnate
3.332
6.743
7.981
9.626
13.817
68
8.137
2.861
Data used
Hissing data
Difference
-6.712
-1.989
-.288
2. 253
6.932
68
.252
3.376
:
Krlglng Std
2.691
2.962
3.176
3.357
4.887
68
3.218
.286
68
a
Zscore
-2.262
-.628
-.868
.629
2.841
68
.858
1.838
Scatter Plot Hlstogran Write Exanfne Quit
Flap of kriging error (differences)
Figure 11-5 Xvalid Results Screen
The Results menu and screen, shown in Figure 11-5, is
displayed when kriging has been completed. The Results screen
contains information about the data file, variables, and the type
of kriging used. Additionally, descriptive statistics are
provided for the original sample values, the kriged estimates,
the kriging standard deviations, the differences (between
estimate and observed), and the zscore. The "zscore" is computed
as the ratio of the difference to the kriging standard deviation.
The Results menu appears at the bottom of the screen, and
provides options to display several graphs, to examine the
individual results, and to save the results to a Geo-EAS data
file. Graph scaling, titles, and labeling are performed
automatically. On a non-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.
Geo-EAS 1.1
11-9
September, 1988
-------
280. •
„ 2«»^
c
f 280.x
b
o
Z ISO. •
120. •
80 '
-\-^~\i< <. '+ "^
1 • • x
r x x -H -+-
^^" 3x" _L
1 • ^ .-^V'] 1
— J— ' **^s 1 1 1
*** 1 1^
N Total
N Hiss
N Used
Mean
Std Dew
ninlnun
25th X
Median
75th X :
Max i nun:
240. 320. 400. 480. 360.
Easting
68
8
68
.252
3.376
-€.712
-1.989
-.288
2.253
6.932
Figure 11-6 Xvalid Error Map
Scatter Plot
The Scatter Plot option provides a choice of displaying one of
two possible scatter plots. When .this option is chosen a two-
valued toggle field containing the choices "Observed vs.
Estimate", and "Estimate vs. Error" is displayed on the message
line. It is used to select the type of scatter plot to be
displayed. Once this choice has been made the appropriate graph
will be displayed. Box plots are drawn opposite to each
coordinate axis to convey information about the frequency
distributions of the observed values and estimates, or estimates
and differences. In both types of graph "+" and "x" symbols are
used to indicate positive and negative estimation errors (same as
the Error Map option described above). An example plot is
displayed in Figure 11-7.
Soattvr Plot
Oo»* Validation for CaAnlun
20.
1*.
xa.
4.
O.
4. 8. 12. t«.
CkiMiUM
20.
Figure 11-7 Xvalid Scatter Plot
Geo-EAS 1.1
11-10
September, 1988
-------
Histogram
The Histogram option provides a histogram (frequency distribution
graph) of the estimation error. An example plot is shown in
Figure 11-8. Histogram class intervals are computed
automatically by the program. A box plot of the differences
appears at the top of the graph. Descriptive statistics are
displayed to the right of the histogram.
EstiMted Variable Cadxiun
i 1 rs 1 1
la. •
a
0 « .
e *•
3
9
t d
b.
-8.
I
-•
nr
_^_
—
*•
9.
r.r.no.: Estl«at.-C
—
Statistics
N Total 68
N Hiss 8
N Used 68
Itoan .252
Sid Dav 3.376
nininun -6.712
25th X -1.989
tied Ian -.288
75th % 2.253
4. 8.
kdxiuM
Figure 11-8 Xvalid Error Histogram
Write
The Write option is used to store the result to a Geo-EAS data
file. When this option is chosen a prompt for the file name
appears on the message line. If the specified file exists, a
Yes/No prompt will provide an option to overwrite, or quit. If
any errors occur while saving the results to the file,
appropriate error messages will be displayed on the message line.
If results were successfully saved, a message will be displayed,
and pressing any key will re-activate the Results menu. The file
created by this option contains seven variables. 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.
Geo-EAS 1.1
11-11
September, 1988
-------
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 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.
1
SB
57
1
44
28
18
12
41
36
46
27
52
55
25
58
4
1
Observation
14.988
16.788
11.588
18.488
12.188
7.288
9.588
18.888
11.688
15.888
14.588
11.688
11.888
11.688
11.688
18.788
Estlnate "
8.188
18.217
5.882
5.828
7.765
3.332
5.658
6.398
8.837
12.482
12.249
9.438
9.793
9.626
9.691
8.791
Difference Kriging Std
-6.712
-6.483
-6.418
-4.572
-4.335
-3.868
-3.842
-3.618
-2.763
-2.598
-2.251
-2.162
-2.887
-1.974
-1.989
-1.989
3.314
2.866
3.498
3.887
3.118
3.489
3.897
3.287
3.875
2.877
2.937
3.223
3.234
2.898
3.163
3.189
Zscore
-2.826
-2.262
-1.835
-1.176
-1.398
-1.134
-1.241
-1.126
-.899
-.983
-.766
-.671
-.628
-.683
-.683
-.614
'•Use t or
* to scrol 1 :
<1> thru <9> to position • or
U i t^^^^^H
Figure 11-9
Xvalid Examine Results Screen
Geo-EAS 1.1
11-12
September, 1988
-------
SECTION 12
KRIGE
12.1
WHAT KRIGE DOES
Krige is an interactive program which performs two-
dimensional kriging. A rectangular grid of kriged estimates is
created and stored in a Geo-EAS data file. Contour plots may be
generated from these gridded estimates with the program Conrec.
Options are provided to control the type of kriging, the
neighborhood search area, the grid spacing and extents, and the
variogram model for each variable kriged. Up to ten variables
may be kriged in each program execution. 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.
12.3 THE MENU HIERARCHY
Krige Prefix
Read Parameters
Options/Execute -
Save Parameters
\ Quit
Data
Polygon
Type
Grid
Search
Variables/Models
Title
Execute
\ Quit
— New Variable
Edit
Delete
\ Quit
Geo-EAS 1.1
12-1
September, 1988
-------
12.4
THE MAIN MENU
fl progran for kriging a grid of estlnates
File Prefix:
Read Paraneter File
Input
Paraneter File= Exanple.Kpf
Saue Paraneter File
Output
Paraneter File: Exanple.Kpf
OptionssExecute
Use the options nenu to select the
Input data file nanei to specify
the Grid and Search Parameters«
to access the UariablesTlodels
screeni and to initiate kriging.
Prefix Read Paraneters
Select progran optionsi Execute
Figure 12-1
Saue Paraneters Quit
Krige Main Screen
The Main screen and menu for Krige, shown in Figure 12-1,
provides options to specify the file prefix, to read or save
program parameter values in a parameter file, and to access the
Krige Options menu, where program parameter values are specified
and kriging is initiated. The menu line appears as follows:
Prefix Read Parameters Options/Execute Save Parameters Quit
Prefix
The Prefix option is used to enter the prefix for the data file
name.
Read Parameters
The Read Parameters option provides a means of loading program
parameter values 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.
Geo-EAS 1.1
12-2
September, 1988
-------
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
Title: Exanple.grd - kriged estl nates of data fron Exanple.dat
Data
Data File : Exanple.dat
Output File : Exanple.grd
Polygon
Polygon File:
Type
Type of Kriging : Ordinary
Point or Block : Block 2x2
Grid Paraneters
X V
Uar table • Easting Northing
Origin : 268.888 128.888
Spacing : 28.888 28.888
nunber : 13 11
Search Paraneters
Hajor Radius : 59.488 I Sectors :
Hi nor Radius = 59.488 flax in Sector:
Ellipse Angle1 .888 f1in. to use :
Distance Type' Euclidean Enpty Sectors '
1
8
1
8
Data Polygon Type Grid Search .lAliilHillilaBJillTHBBI Title Execute Quit
This option Invokes the Uariables and Uarlogran Models screen
Figure 12-2 Krige Options Screen
The-Options screen and menu (Figure 12-2) has the options to
specify the parameters to be used for kriging, and to initiate
the kriging process. The menu line appears as follows:
Data Polygon Type Grid Search Variables/Models Title Execute Quit
Geo-EAS 1.1
12-3
September, 1988
-------
Data
The Data option is used to specify the name of the Geo-EAS data
file whose values will be used for kriging, and the name of the
Geo-EAS output file of gridded estimates. The screen 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. This file should contain one or more
lists of polygon vertices which form closed polygons. Each
vertex list is preceded by a flag which indicates if it is to be
treated as an inclusive or exclusive polygon. No estimates may
be kriged within an exclusive polygon boundary, and none may be
produced outside an inclusive boundary. 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.
Geo-EAS l.l . 12-4 September, 1988
-------
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 "Block NxN"
choices is selected, 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, and Number 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.
Geo-EAS 1.1 12-5 September, 1988
-------
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. The
choices available are "Euclidean" (the default), and
"Variogram". Neighboring samples are eliminated from
consideration when the Max Pts/Sector (Maximum points per
sector) criterion is exceeded in a given sector. If this
should occur, only the "closest" neighbors are kept. If
the "Euclidean" distance type is chosen, neighbors are
eliminated based upon the euclidean distance from the point
to be estimated ellipse center. If "Variogram" distance is
chosen, the variogram function value (as specified by the
Model parameters) for the computed distance is used as the
criterion for elimination 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 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.
Geo-EAS l.i 12-6 September, 1988
-------
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.
Geo-EAS 1.1 12-7 September, 1988
-------
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 Title option is used to indicate the descriptive title to
store in the output file of gridded estimates. It provides
access to a 60 character alphanumeric field for storing the
title. A default title is constructed from the data file name
and the output file name. Any valid alphanumeric character
string may be entered.
Execute
The Execute option is used to initiate kriging. All parameters
must be specified before kriging may begin. Several "Debug
Options" (described below) are enabled or disabled with the
, 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.
If your personal computer is equipped with the proper
graphics hardware, a graphics display (shown in Figure 12-3) is
generated when the Execute option is selected. In this display
the original sample locations are represented by the "x" symbol.
As each point is kriged, the estimates and associated results are
displayed at the bottom of the screen (except in Hercules-
equipped systems) and the point or block estimates are plotted
with a symbol which indicates the quartile of the estimate. On
EGA equipped computer systems, these symbols and the sample
values are also color coded. A legend is displayed at the right
of the screen showing the symbols and corresponding quartile
cutoff values. If your computer system has no graphics
capability, no graph is displayed, and the results are displayed
at the bottom.of the Krige Options screen.
During the kriging process the debug displays (described
below) 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.
Geo-EAS i.l 12-8 September, 1988
-------
.
-
-
-
.
.
Block krisrinsr: CadMiun
>•::::«: » {.*:::« :: e K: :x:: •»
• • • *«• • • ^.« ••••• • • ••••••• •
.... • ••..••••» £;:•••;•
t • . . * ••..«••••: r: :::::•
• K .«...• • * •
N
» x y z*
143 588. 328. 8.87
C*dMiUM
< S.3Q0
I : < 7.600
::: < iQ.see
SJI! >=10.8B9
X - Hlssinar
ok N
2.28 3
Figure 12-3
Kriging Display
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.
Geo-EAS 1.1
12-9
September, 1988
-------
12.6
THE VARIABLES/MODELS MENU
List
of
Uariables
to
Krlge
Uariablns and node Is Selection
Uariable : Cadniun
Global Mean :
1 Cadniun 3
2
3
4
S
6
7
8
9
IB
Uarlogran ftodel Paraneters
Mugget : 4.598
D Type Sill Ualue ftajor Range HI nor Range Angle
1 Exponent.
2
3
4
13.588
388.888
188.888
Mew Uariable ilCTIH Delete Quit
Select a variable and edit the uariogran nodel paraneters
Figure 12-4
Krige Variables/Models Screen
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.
*** Note *** it is possible to krige the same variable more
than once; the output file will then contain duplicate
variable names.
Geo-EAS 1.1
12-10
September, 1988
-------
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 move the cursor bar to
fields in the Model area. To exit the Model area, move the
cursor bar out of the top or off to the left of the area, using
the , or keys. If any errors are made when entering
variogram model parameters an error message will be displayed and
the cursor bar will be placed at the problem field. The screen
fields accessed from this option are:
Nugget - A numeric field for entering the nugget value for the
variogram model. Only values greater than or equal to zero
may be entered. The 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 - 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
isrunimportant; neither* do they need to be in a contiguous
order on- the screen.
Sill - A numeric field for entering the sill value for a
variogram structure. A non-zero, non-negative value is
required here. 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.
Geo-EAS 1.1 12-11 September, 1988
-------
Major Range - A numeric value for entering the longest range of
influence of the variogram structure. The Major Range must
be non-zero, and non-negative. This may be thought of as
similar to the R Major parameter described in 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 different purposes, although the
parameters which describe them are v-he same
Minor Range - A numeric field for indicating the length of the
minor (shorter) range of the variogram ellipse. This value
must be non-zero, non-negative, and less than or equal to
the Major Range. The default value is the Major Range
value. If the two ranges are equal, an isotropic variogram
structure is defined. If they are not equal, the two ranges
are used to determine the ratio of anisotropy.
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.
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.
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:
Geo-EAS 1.1 12-12 September, 1988
-------
Plot of N«ifirhbox»«
Point: < 3&O.O00, i8O.aoo>
320.
288.
240.
200.
160. •
12O. •
80.
240.
320.
400.
Eastinar
480.
S60.
Figure 12-5 Krige Debug: Search Area Display
- 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.
Debug results for variable
Point kriged is
:Cadniun
:( 368.869,
388.888)
2(1) fl(I.J):
18,294
8,677
9,954
5,866
5,482
3,838
6,713
1,888
18,888
6,561
9,328
7,548
7.135
3,923
~ 7,383
1,888
6,561
18,888
8,228
3.789
3.513
1.918
4.755
1,888
9,328
8,228
18,888
5,312
5,489
2,819
5,347
1,888
7.548
3.789
5.312
18.888
9.635
6.977
7.489
1.888
7.135
3,513
5,489
9,635
18,888
6.611
5.588
1,989
3.923
1.918
2,819
6,977
6,611
18,888
4.297
1,888
7,383
4.755
5.347
7.489
5,568
4.297
18.868
1,868
1,888
1,888
1,888
1,888
1,888
1,888
1,888
iDDD
Figure 12-6 Krige Debug: System of Equations Display
Geo-EAS 1.1
12-13
September, 1988
-------
ocroll lock> - 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.
Debug results for uariable :Cadniun
Point kriged Is =( 368.888. 188.888)
X(l)
378.
368.
378.
358.
334.
334.
346.
368.
Neighbors'
Estimate:
•"k:
"'K:
V
188.
195.
165.
283.
194.
163.
218.
216.
7.58
1.62
2.61
ti) U(l) Distance
6.18 9.68
6.88 15.8
6.78 17.8
8.38 24.9
11.6 - 29.9
8.78 31.4
18.8 33.3
18.1 36.8
8 Z Weights: 1.888
CUU: 11.389
£ M1B21: 9.298
V- -.518
um
.384
.142
.165
.324E-81
.123
.124
.128E-81
. 171E-81
B2(l)
11.2
8.68
8.58
6.79
8.22
7.62
5.48
4.63
Figure 12-7 Krige Debug: Kriging Weights Display
- 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 1.1
12-14
September, 1988
-------
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.
13.3
THE MENU HIERARCHY
Postplot Prefix
-Data
Variables
Options
Graph Options Axis Parameters
Tick Parameters
Graph Limits
Titles/Labels
Reset
\ Quit
Execute
\ Quit
Geo-EAS 1.1
13-1
September, 1988
-------
13.4
THE MAIM 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
A progran for plotting 20
File Prefix : C'^CeoEASMJa^
Data '• Exanple.dat
Uariables
X coordinate uarlable Easting
V coordinate oariable Northing
Uariable to post Cadniun
Options
Include Values : Mo Size : 5
Scale Factor : 18" 8
tt Decinals : 1
Include Synbols: Yes Size : 4
sanple locations and values
ttetacode File : Hetacode.net
Execute
plot. The plot ulil be saued in
the file specified.
Prefix Data Uariables Options Graph Options
Generate the plot
Quit
Figure 13-1 Postplot Main Screen
Prefix
The Prefix option is used to enter the prefix for file names.
Data
The Data option is used to enter the name of a Geo-Eas data file.
Variables
The Variables option allows the selection of variables that are
to be used as the X and Y coordinate values, and the sample
values to po»t-:—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.
Geo-EAS 1.1
13-2
September, 1988
-------
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.
Variable to post - 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.
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 is "4".
These choices work well on the screen, however a smaller
size might be more suitable for output to a plotter.
Scale Factor - A toggle field for selecting the scaling factor to
apply to the values to be plotted. The choices available
range from "10"-4" to "10*4". The scaling factor shifts the
decimal place left or right in the plotted value. For
example a scale factor of 10~4 applied to a value of 7.208
would result in the value 72080 being plotted. If the
Include Values field is set to "No", this choice is ignored.
If the default of "10*0 "is used the decimal place will not
be shifted.
# Decimals - 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 two-valued (Yes/No) toggle field to enable or
disable the plotting of symbols at the sample locations.
The choices available are "Yes" - plot symbols, "No" - do
not plot symbols. If the value is "Yes" (the default) four
different symbols in four different colors will be plotted
to represent the values within their quartiles. A legend is
also plotted to show the quartile cutoff values, the
symbols, and their corresponding colors.
Geo-EAS 1.1 13-3 September, 1988
-------
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.
Po*tplot of Cadmium from data fil« Exompl«.dot
ZOO
.r
200
too
1.1
2nd Qoortil.:
.Sfd QuartCte:
*w> Ouartite
a
x a a
-365-
Coating (f««t)
.000 * +
9.3OO < X
7.800 < a
10.000 < •
coo
9.3OO
T.8OO
1O.SOO
1 9. TOO
Figure 13-2 Example Post Plot
Geo-EAS l.l
13-4
September, 1988
-------
13.5
THE GRAPH OPTIONS MENU
Paran t
Graph Units
Hiii •
flax :
Titles'Labels
nain title
Subtitles
X Label
V Label
l^^jyyyjgjyi^
Axis Style: Full
X V
258 188
SOB , 358
Tick Paraneters
Base :
Type :
Label :
Fraction:
Exponent :
Auto
Auto
Auto
Auto
Auto
Auto
Auto
Auto
Auto
Auto
: Postplot of Cadniun fron data file Exanple.dat
•
: Easting (feet)
: northing Cfeet)
Axis Paraneters Tick Paraneters
Title/Labels Reset Quit
Select the options for the graph background
Figure 13-3 Postplot Graph Options Screen
The Graph Options screen and menu, displayed in Figure 13-3,
provides control over the "graph background" parameters. These
parameters are used to specify the axis style, the graph limits,
titles and axis labels, and the tickmark labeling and spacing.
The menu line appears as follows:
Axis Parameters Tick Parameters Graph Limits Title/Labels Reset Quit
Axis Parameters
The Axis Parameters option allows the selection of the type of
axis style for the background of the plot. The screen field
accessed from this option is a toggle field. Choices 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 of ten. An excerpt from the
NCAR documentation on tickmark parameters is included in the
appendices. Certain incompatible combinations of parameter
choices will result in no labels being plotted or error messages
Geo-EAS 1.1
13-5
September, 1988
-------
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 "Auto1" 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 * 10~k
• Base~k
Note: "k" is an arbitrary integer computed by the program.
The default value is "Auto" for both axes.
Label - Two toggle fields for selecting the format of numeric
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
Fraction - Two numeric fields for entering the number of
significant digits to display in the numeric axis labels.
Exponent - Two numeric fields for entering the value of the
exponent in the numeric axis labels.
Table 13-1 shows examples of the types of numeric tick mark
labels that can be produced, using combinations of choices for
the Base, Type, Label, Fraction, and Exponent parameters. The
labels were_produced using the Example.dat data file with Easting
as the X variable and Northing as the Y variable. Remember that
certain combinations of parameter values are 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.
Geo-EAS 1.1 13-6 September, 1988
-------
Base
Auto
Auto
2.
2.
Auto
3.6
Auto
5.
Type
•Base*k
•Base*10~k
•Base*10~k
•Base'k
•Base~k
•Base*10~k
•Base'k
•Base'k
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
.2 x 103
64
.2 X 103
30
100.01 X 10°
r s.o2
\
Table 13-1
Graph Limits
Numeric Tickmark Label Examples
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 - 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.
Max - Two numeric fields for entering the maximum coordinate
value to be used on the X and Y axes. The default values
displayed are determined from the variables selected as the
X and Y coordinate values.
Titles/Labels
The Titles/Labels option allows you to enter the title and labels
for the graph. The Hershy character sets of 33 fonts are used
for plotting alphanumeric labels. Also, certain "special
characters" may be embedded in the title or label which control
selection of—ai-ternate 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:
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.
Geo-EAS 1.1
13-7
September, 1988
-------
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 1.1 13-8 September, 1988
-------
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
Read Parameters
Opt i ons/Execute
— Data
Variables
Symbol/Line
Regression
Legend
Graph Options
Execute
\ Quit
Save Parameters
\ Quit
Axis Parameters
Tick Parameters
Graph Limits
Titles/Labels
Reset
\ Quit
Geo-EAS 1.1
14-1
September, 1988
-------
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
An X-V graph plotting progran
File Prefix: C:vGeoEASVDataN
Input Parameter File : exanple.xpf
Output Paraneter Flle: exanple.xpf
Options
Use this option to select control
paraneters. A nenu of additional
options will be displayed.
Prefix Read Paraneters
Saue Paraneters Quit
Ed it i or enter parameter values
Figure 14-1 Xygraph Main Screen
Prefix
The Prefix option is used to enter the prefix for file names.
Read Parameters
The Read Parameters option is used to enter the input parameter
file name.
Options/Execute
The Options/Execute option provides access to the Options screen
and menu. See the section on Options below for more information.
Save Parameters- -
The Save Parameters option is used to enter the name of the
output parameter file. If the specified file already exists,
a Yes/No prompt is provided to quit or proceed. The parameter
file will contain the current parameter values. It will be saved
for future use as an input parameter file.
Geo-EAS 1.1
14-2
September, 1988
-------
14.5
THE OPTIONS MENU
Data File : exanple.
tletacode File : Metacode
Uar tables
X Uariable
flrsenic
V Uariables
Lead
dat
• net
Synbol/Llne Type
Synbol Type
1
2
3
4
5
6
Line Type
8
B
8
8
8
8
Color
Black
Blue
Red
Vellow
Green
Broun
Regression = Ves
Legend : Hone
Execute
Use this option to create
the graph. The graph
be saued In the file
specified.
uill
Data Uariables Synbol/'Line Regression Legend Graph Options J3TBi3tn!l Quit
Generate the graph
Figure 14-2 Xygraph Options Screen
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
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 1.1
14-3
September, 1988
-------
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:
Symbol Type - Six toggle fields for selecting the type of symbol
to plot. There are six choices available ("0" to "6"). A value
of "0" indicates that no symbols are to be plotted. The default
Symbol Types for the six variables are "1" through "6".
Line Type - Six toggle fields for selecting the type of line to
plot for each variable. There are six choices available ("0"
through "6"). A value of "0" indicates that no line is to be
plotted. The default Line Type for all six variables is "0".
9
*
O No lln«
Figure 14-3
Xygraph Symbols and Line Types
Color - Six toggle fields for selecting the color to plot the
symbol and/or line pattern. The choices available are
"Black", "Blue", "Red", "Yellow", "Green", "Brown". The
default color is unique for each variable.
Regression
The Regression option provides access to a two-valued (Yes/No)
toggle field—to—enable or disable the calculation of linear
regression. If the value is "Yes" linear regression is only
calculated for the first Y variable. The regression line and the
regression coefficients are plotted on the graph. The
coefficients are the slope and intercept of the line represented
by the equation Y = Slope * X + Intercept. The R Squared value
(a measure of correlation) is also plotted. The default is "No".
Geo-EAS 1.1
14-4
September, 1988
-------
Legend
The Legend option provides access to a toggle field that is used
for selecting the position of the graph legend. The choices
available are "None" (no graph legend), "Bottom" (at the bottom
of the graph), and "Right" (at the upper right-hand corner of the
graph). The default position is "None" (no legend).
Graph Options
The Graph Options option provides access to the Graph Options
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.
Example.dot — Geostattstical Environmental
4-OO r
3OO
2OO
1OO
Figure 14-4
Example Xygraph Plot
Geo-EAS 1.1
14-5
September, 1988
-------
14.6
THE GRAPH OPTIONS MENU
pmilBHiiHiiii
Axis Style: Half
Graph Lin its
X V
nin 254.488 118.888
Max 492.888 3)5.888
Scale Linear Linear
Tlttes'Labels
tlain title: Exanple XVGRAPH Plot
Subtitles:
X Label: Easting (feet)
V Label: Northing (feet)
Tick Paraneters
Base : Auto
Type : Auto
Label : Auto
Fraction: Auto
Exponent : Auto
Auto
Auto
Auto
Auto
Auto
Tick Paraneters Graph Linits Title/Labels Reset Quit
Select style for X and V axes
Figure 14-5 Xygraph Graph Options Screen
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-tickraark labels to be placed along each axis. This
is accomplished with a set of closely inter-related parameters
which control the format of the labels. The default values are
initially set to "Auto", and provide adequate labels for most
data. With the appropriate selection of parameter values,
however, many useful labels may be constructed, including
fractions and superscripted powers of ten. An excerpt from the
NCAR documentation on tick parameters is included in the
appendices. Certain incompatible combinations of parameter
choices will result in no labels being plotted or error messages
generated by the NCAR Autograph utility. These errors will cause
Geo-EAS 1.1
14-6
September, 1988
-------
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 * 10*k
• Base~k
Note: "k" is an arbitrary integer computed by the program
The default value is "Auto" for both axes.
Label - Two toggle fields for selecting the format of numeric
label to be used at the major tick marks along the X and Y
axes. The available 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.
Geo-EAS 1.1 14-7 September, 1988
-------
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.
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 - 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 parameters to their
default values.
Geo-EAS 1.1 14-8 September, 1988
-------
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
Conrec
Prefix
Read Parameters
Option/Execute —
Save Parameters
\ Quit
Data
Variables
Graph Options -
Axes Parameters
Tick Parameters
Titles/Labels
Annotation
\ Quit
Contour Options — New Levels
Edit Levels
Labeling
Dash Pattern
Annotation
Execute Spline
\ Quit \ Quit
Geo-EAS 1.1
15-1
September, 1988
-------
15.4
THE MAIN MENU
A contouring program for grldded data
File Prefix: c:NCeoEASM)ataN
Input Parameter File : Example. cpf
Output Paraneter Flle: Exanple.cpf
Use this submenu to specify the
data file and uar tables* to
access the Contour and Graph
options screens, and to u leu
the contour plot.
Data File Mane: Exanple.Grd
X Uarlable Easting
V Uarlable Northing
Contour Uarlable *Cadr»lun
Graph Units X
1 Pts. : 13
nininun: 268. 898
Maxinun: 589.888
Size: 28.808
V
11
128.888
328.888
28.888
Prefix Read Paraneters .i\\UUAM!KlJ«m
Ed Iti or enter paraneters
Figure 15-1
Saue Paraneters Quit
Conrec Main Screen
The Main screen and menu (Figure 15-1) has the options to allow
specification of the input and output parameter file names. The
menu line appears as follows:
Prefix Read Parameters Options/Execute Save Parameters Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Read Parameters
The Read Parameters option is used to enter the input parameter
file name.
Options/Execute
The Options/Execute option provides access to the Options menu.
See the section on Options below for more information.
Save
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.
Geo-EAS 1.1
15-2
September, 1988
-------
15.5
THE OPTIONS MENU
fl contouring progran for gridded data
Pile Prefix: C^eoEAS^Data^
Input Paraneter File : Exanple.cpf
Output Paraneter File: Exanple.cpf
Use this option to Uieu the graph.
The plotting instructions will be
saued in a special file called a
"netacode File". Other software
nay be used to produce plotter
hardcopy fron this file.
Data File Mane: Exanple.Grd
X Uariable : Easting
V Uariable : Northing
Contour Uariable : *Cadniun
Graph Units X
• Pts. : 13
nininun: 268.888
naxinun: 588.888
Si2e: 28.888
V
11
128.888
328.888
28.888
Data Variables Graph Options Contour Options
Uieu the contour plot
Quit
Figure 15-2
Conrec Options Screen
The Options screen and menu, shown in Figure 15-2, has the
options to allow specification of the data file name and the
selection of variables to be used. The menu line is as follows:
Data Variables Graph Options Contour Options Execute Quit
Data
The Data option is used to enter the data file name. The file
must have coordinate variables with values that form a complete
grid. An example of such a file is the file of kriged estimates
produced by the program Krige. Krige creates a file with a .grd
extension by default. This is a Geo-EAS data file which contains
gridded data.
Variables
The Variables option allows selection of the variables that are
to be used as the X and Y coordinate values and the variable to
be contoured. The choices available are the variable names as
specified in_the data file. If a grid could not be formed from
the data ari~i~rro~f 'message is displayed. After the grid is formed
a Yes/No prompt is displayed which allows computation of defaults
for the Graph Options and Contour Options screens. If the
response is "Yes" default values for Contour Options and Graph
Options options will replace any previous entered values on these
screens. If the response is "No" and no contour levels have been
set, an error message will occur when the Execute option is
selected. The screen fields accessed from this options are:
Geo-EAS 1.1
15-3
September, 1988
-------
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.
Krlglng estimates produced from data ffle Example.
Contoura for •Codmfum
330.
28O. MO. »*O.
»3OL *«OL
Figure 15-3 Example Contour Plot
Geo-EAS 1.1
15-4
September, 1988
-------
15.6
THE GRAPH OPTIONS MENU
I^IBHH^HizaaUiiEisa
fixes Paraneters Full Full
Tick Paraneters
8 Major Ticnark Diuisions 6 4
B Minor Diuisions ' Major 4 5
Ticknark Label Fornat (FIB. 8) (FIB. 8)
Tlcnark Label Size S . 5
Graph Lin its
X
B: 13
Min: 268.888
Max: 588.888
Size: 28.888
Titles'Labels Main Center Subtitles: Center
Main Title: BBlBExanple COMREC Contour Plot
Subtitles: BBBSflrsenic Estt nates fron Exanple.Grd
: BB87Data Krlged fron Exanple.dat - Arsenic
: B887 June 6th, 1988
X Axis: BBlBEasting
V Axis: BBlBMor thing
V
11
128.888
328.888
28.888
Size
9
7
4
4
7
7
Axes Paraneters Tick Paraneters Tltles^Labels
Enable'Dlsable the annotation option
Figure 15-4
ilHlMMili'lll Quit
Conrec Graph Options Screen
The Graph Options screen and menu (Figure 15-4) provides control
over the "graph background". Options are available to select the
axis style, the format for tickmark labeling and spacing, and the
character size and orientation of the graph titles and axis
labels. The menu line appears as follows:
Axis Parameters Tick Parameters Titles/Labels Annotation Quit
Axis Parameters
The Axis Parameters option allows selection of the type of axis
style for the X and Y axes. The screen field accessed from this
option is Axis Style which consists of two toggle fields. The
choices available are "Half" (left and bottom axes only), "Full"
(left, right, top, and bottom axes) and "Grid" (the same as
"Full", but the major tickmarks extend across to the opposite
axis). The Axis Style for the axes are independent of each
other: for example if the Axis Style is "Half" for the X axis and
"Full" for the Y axis, the Bottom, Left, and Right axes would be
drawn. The default value is "Full" for both the X and Y axes.
Tick Parameters'
The Tick Parameters option allows the specification of the
spacing and format of the numeric tickmark labels on the X and Y
axes. The screen fields accessed from this option are:
# Major Tickmark Divisions - Two numeric fields for entering the
number of major tickmark divisions along the X and Y axes.
The default may be calculated by the program when the
Variables option is selected.
Geo-EAS 1.1
15-5
September, 1988
-------
# Minor Division/Major - Two numeric fields for entering the
number of minor tickmark divisions per major division along
the X and Y axes. The default may be calculated by the
program when the Variables option is selected.
Tickmark Label Format - An alphanumeric field which may contain
up to 10 characters for entering a FORTRAN format specifier
which describes how the label is to be printed. The format
must a valid FORTRAN format for a REAL value with a format
width no greater that 10. A default format is constructed
from the grid coordinate values. This format should be
adequate for most purposes. If an invalid or unsuitable
format specifier is entered an error message is displayed.
For more information on FORTRAN format specifiers, refer to
a FORTRAN reference manual.
Tickmark Label Size - A toggle field used for selecting the
character size of the tickmark labels. The choices
available are "1" to "10". The default size is "3". This
value works well on the screen, however a smaller size might
be more suitable for output to a plotter.
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.
Geo-EAS 1.1 15-6 September, 1988
-------
Y Axis - 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.
Size - Six toggle fields for selecting the character size for the
labels. The choices available are "0" to "10" where "0" is
the smallest and "10" is the largest character size. The
default for the Main Title is "6". The default for the
first and second subtitles and the X and Y axes is "5". The
default for the third subtitle is "4". These choices work
well on the screen, however smaller sizes might be more
suitable for output to a plotter.
Annotation
The Annotation option allows the user to suppress the axes,
titles, and labels for the graph. The screen field accessed from
this option is a toggle field that is displayed on the message
line. The choices available are "Plot axes and titles", or "No
annotation" (do not plot axes and titles) . The default is "Plot
axes and titles".
15.7
THE CONTOUR OPTIONS MENU
ll.HM.IUJtJ.Jll.l.y Saline
Starting Contour Ualue
flax i nun Contour Ualue
Contour Leuel Increment
It Contour Leuels
Labeling Option
Label Skip Factor
First Leuel to Label
Label Size
Tension: 5.8
.888
2.488
.488
Off
1
1
7
Dash Pattern : — —
Dash Cutoff : .888
B Rep'Label : 5
Annotation Option: tto Annotation
Character Size: 8
Contour Leuel
1
2
3
4
5
6
7
8
9
18
11
12
13
14
15
16
.888
.488
.888
1.288
1.688
2.888
2.488
Label
.8
.4
.8
1.2
1.6
2.9
2.4
New Leuels iJBMJIBBnH Labeling Dash Pattern Annotation Spline Quit
Edit contour levels and labels
Figure 15-5 Conrec Contour Options Screen
The Contour Options screen and menu (Figure 15-5) has options to
allow specification of the contour levels, labels, the skip
factor , label size and the selection of a dashed line pattern.
The menu line appears as follows:
New Levels Edit Levels Labeling Dash Pattern Annotation Spline Quit
Geo-EAS 1.1
15-7
September, 1988
-------
New Levels
The New Levels options allow you create a. list of equally spaced
contour values and labels. The defaults for these screen fields
may be calculated by the program when the Variables option is
selected. The program calculates the contour levels and the
corresponding labels based on the values from these fields. The
screen fields accessed from this option are:
Starting Contour Value - A numeric field for entering the lowest
contour level.
Maximum Contour Value - A numeric field for entering the highest
contour level.
Contour Level Increment - A numeric field for entering the
increment value between the contour levels.
Edit Levels
The Edit Levels option allow you to 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".
First Level to Label - A ten-valued ("1" .. "10") toggle field
for selecting the first contour level to label. The default
is "1".
Label Size - A ten-valued toggle field ("1".."10") for selecting
the contour label character size. The default is "6".
Geo-EAS l.l 15-8 September, 1988
-------
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
it it 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
It C II
•J .
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.
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
Spline
The Spline option allows the specification of the amount of
smoothing of the line segments. The screen field accessed from
this option is a numeric field. Acceptable values range from 2.5
to 30. The larger the Spline Tension value the less smoothing of
the line. A value of 30 disables smoothing. Smooth contours
generally look better; but because the contour lines are smoothed
independently, smoothing results in contour lines which may
intersect. The default value is 15.0.
Geo-EAS 1.1 15-9 September, 1988
-------
Geo-EAS 1.1 15-10 September, 1988
-------
SECTION 16
VIEW
16.1 WHAT VIEW DOES
View displays on the screen the graphs contained in metacode
files. The graphs can be displayed on a EGA, CGA, or Hercules
graphics system. Color graphs are viewed on EGA systems. On CGA
and Hercules systems monochrome graphs are displayed.
16.2 THE MENU HIERARCHY
View Prefix
File
Scale
Execute
\ Quit
16.3 THE MAIN MENU
The Main screen and menu, shown in Figure 16-:!, 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 _op_tio.n.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.
Geo-EAS 1.1 16-1 September, 1988
-------
A netacode translator Tor EGA. CGA( or Hercules graphics configuration
File Prefix : C^GeoEAS^DataN
netacode Filenane : Conrecl.net
Scale = Square
Adaptor : EGA (648 x 358)
Execute
Use this option to display the
plot.
Prefix File Scale
Display the plot
Quit
Figure 16-1 View Main Screen
Scale
The Scale option is used to select the type of plotting area to
use when displaying the graph. The screen field accessed from
this option is a toggle field. The choices available are
"Square" (the original scaling of the graph), and "Rectangle" (the
graph will be stretched to fit the 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 1.1
16-2
September, 1988
-------
SECTION 17
HPPLOT
17.1 WHAT HPPLOT DOES
Hpplot translates the device independent plotting instructions in
metacode files into a file of HPGL plotting commands. The output
file can be routed to a HP plotter by setting up the serial port
(COM1) by running the batch file HPSETUP.BAT and then using the
DOS PRINT command to send the file to the plotter. The HP
plotters supported are:
HP 7470 - 2 pen plotter
HP 7475 - 6 pen plotter
HP 7450 - 8 pen plotter
If the HP 7470 is used for plotting the graph will be plotted in
two pen colors, the program does not prompt for pen changes.
17.2 THE MENU HIERARCHY
Hpplot Prefix
File
Scale
Execute
\ Quit
17.3 THE MAIN MENU
The Main screen and menu (Figure 17-1) has the options to allow
specification of the metacode and output file names, and the
plotting area. The menu line appears as follows:
Prefix File Scale Execute Quit
Prefix
The Prefix option is used to enter the prefix for file names.
Geo-EAS 1.1 17-1 September, 1988
-------
Translates a netacode file Into HPGL plotting instructions
File Prefix : C^GeoEAS>DataN
Input Fllenane : Conrecl.net
OutDut Fllenane: ^,111.. JBli »fl|
Scale: Square
Enter the output file nane
Prefix File Scale Execute Quit
Figure 17-1 Hpplot Main Screen
File
The File option is used to enter the metacode file name. The
screen field accessed from 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 Postplot.
Scale
The Scale option is used to select the type of plotting area to
use when displaying the graph. The screen field accessed from
this option is a toggle field. The choices available are
"Square" (the true scale of the graph), and "Rectangle" (the
entire screen). The default is "Rectangle".
Execute
When the Execute option is selected, you will be prompted for a
output file name before the output file is created. The output
file name entered must be up to 14 characters. This 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.BAT (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 1.1
17-2
September, 1988
-------
APPENDIX A
REFERENCES
Journel, A.G. and C.H. Huijbregts, 1978, Mining Geostatistics,
Academic Press, London.
David, M., 1984, Geostatistical Ore Reserve Estimation, Elsevier,
Amsterdam.
Clark, I., 1979, Practical Geostatistics, Applied Science
Publishers, 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-EAS 1.1 A-l September, 1988
-------
Geo-EAS 1.1 A-2 September 12, 1988
-------
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 'None1 turns off the numeric labels on the
axis specified. The other parameters, are then ignored.
Scientific Labeling
- Setting Label to 'Scien.' selects scientific notation. Each
numeric label is written in the form:
[-] [i] [•] [f] * 10 e
Where brackets enclose portions which may be independently
present or absent and 'e1 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
•i1, thus also specifying the value of the exponent 'e1. IF
Exponent has a value less than or equal to zero, 'i1 is
omitted^.-If.Exponent is less than zero and has the integral
absolute value 'n1, the fraction 'f is forced to have
'n1 leading zeroes.
The parameter Fraction specifies the number of characters in
•f. If Fraction is less than or equal to zero, 'f1 is
omitted. If Fraction is less than zero, the decimal point
is omitted.
If "[i] [-] [f]" has the value '!.', the first part of the
label is omitted, leaving only '10 e1.
Geo-EAS 1.1 B-l September, 1988
-------
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:
C-] [i] CO [f] * 10 e
Where brackets enclose portions which may be independently
present or absent and 'e1 is a superscript exponent.
The parameter Exponent specifies the integral value of the
exponent ' e ' .
The parameter Fraction specifies the number of characters in
•f . If Fraction is less -than or equal to zero, 'f is
omitted. If Fraction is less than zero, the decimal point
is omitted.
If the label is exactly zero, the single character '0' is
used.
- If the parameter Type has the value • Base*10~k. Each
numeric label is written in the form:
[-] [i] [.] [f] * 10 e
The parameter Exponent specifies the integral value of the
exponent 'e' when 'k1 equals '0.'. The value of 'e1 is
Exponent plus 'k1.
The parameter Fraction specifies the number of characters in
'f . If Fraction is less than or equal to zero, 'f is
omitted. If Fraction is less than zero, the decimal point
is omitted.
If the label is exactly zero, the single character *0' is
used.
- If the parameter Type has the value • Base'k. Each numeric
label is written in the form:
[-] [i] [-]
The parameter Exponent is ignored. The value of 'e1 is 'k1.
The parameter Fraction specifies the number of characters in
'f. If Fraction is less than or equal to zero, 'f1 d.s
omitted. If Fraction is negative, the decimal is omitted.
Geo-EAS 1.1 B-2 September, 1988
-------
(Note that ' [i] [.] [f]1 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
'f1. If Fraction is less than or equal to zero, 'f1 is
omitted. If Fraction is less than zero, the decimal point
is omitted. If the label is exactly zero, the single
character '0' is used.
- If the parameter Type has the value • Base* 10 "k. Each
numeric label is written in the form:
C-] [i] [.] [f]
The parameter Fraction specifies the number of characters in
'f1 when 'k1 is zero .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 = 3.6, and k ranges from
-3 to +3 ; the labels produces are
.0036, .036, .36, 3.6, 36. 360., and 3600.
- If the parameter Type has the value • Base'k. Each numeric
label is written in the form:
[-] [i] [-]
if 'k1 is greater than or equal to zero, and in the form
[-] V [i] CO [f]
if 'k1 is less than zero.
The parameter Fraction specifies the number of characters in
•f when 'k1 is equal to 1.. If Fraction is less than or
equal to zero, 'f1 is omitted. If Fraction is less than
zero, the decimal point is omitted. For example, if
Fraction = -1., Base = 2., and k ranges from -4 to +4; the
labels produced are:
1/16, 1/8, 1/4, 1/2, 1, 2, 4, 8, 16
Geo-EAS 1.1 B-3 September, 1988
-------
Geo-EAS 1.1 B-4 September, 1988
-------
APPENDIX C
Hershy character Font Tables
The Hershy character set consists of 33 different character
fonts, numbered 0 through 32. This information is stored in a
machine-readable file called 'HERSHY.BAR', which is included with
the software distribution. The font descriptions indicate the
extent to which the characters contain tapered segments (simplex,
duplex, complex, triplex, or gothic), and the size of the
characters (cartographic, indexical, principal, or centered
symbol). The following table lists available fonts and font
codes.
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
Geo-EAS 1.1 C-l September, 1988
-------
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:
11 - 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)
Font 884
Font 829
<3ro«tcitis11ral
Font B87
Underlining
Geoatotistleal Environmantol Assessment Software
Special characters fro* font 818 and font BBS
Special characters — >, £, f, rr
Superscr ipting us ing the > character: Easting (n>2)
Easting (m*>
Figure C-l
Example font selection codes
The following table illustrates all font groups, and symbols
within each group:
Geo-EAS 1.1
C-2
September, 1988
-------
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 contructed 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 to exclude computation of an estimate at that location.
The rule which governs processing of multiple polygons is this:
No flag may be changed to Include an estimate which has been
Excluded by a previous polygon.
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).
Geo-EAS 1.1 D-l September, 1988
-------
ASCII Character
Font
1 1
12
13
14
15
16
17
18
19
20
21
I $ & ' C > *
MNOPQRST
+ , - / 0 1 2
UVWXYZab
3456789
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