United States
Environmental Protection
Agency
Robert S. Kerr Environmental
Research Laboratory
Ada, OK 74820
Research and Development
EPA/600/S8-90/004 May 1990
&EPA Project Summary
Geostatistics for Waste
Management: A User's
Manual for the GEOPACK
(Version 1.0) Geostatistical
Software System
S.R. Yates and M.V. Yates
GEOPACK, a comprehensive user-
friendly geostatistical software
system, was developed to help in the
analysis of spatially correlated data.
The software system was developed
to be used by scientists, engineers,
regulators, etc., with little experience
in geostatistical techniques and still
satisfy the requirements of more
advanced users. By using GEOPACK,
and spending a little time becoming
familiar with geostatistics, end-users
will be able to include these
geostatistical techniques in their
work and research environments.
This Project Summary was
developed by EPA's Robert S. Kerr
Environmental Research Laboratory,
Ada, OK, to announce key findings of
the research project that is fully
documented in a separate report of
the same title (see Project Report
ordering information at back).
Introduction
Using the geostatistical techniques in
the analysis of spatially correlated data
generally requires the use of a computer
to handle the large number of samples
and carry out the lengthy calculations.
Unless one knows someone who is
willing to provide the necessary computer
programs, one is faced with the difficult
task of finding, purchasing or developing
the required computer software. Although
there are a number of practicing
geostatisticians who undoubtedly have
access to the necessary programs, these
programs are not generally available or
they are proprietary codes. Often, the
programs which are developed for
research purposes are subject to limited
availability and are difficult for others to
use or modify for purposes other than
those for which they were originally
designed.
GEOPACK was developed with the
philosophy that geostatistical software is
needed that can be used by individuals
with a minimum level of geostatistical
expertise and yet can also satisfy the
needs of more sophisticated users. The
specific objectives in developing this
program were:
(1) develop geostatistical software for
individuals without a great deal of
geostatistical training and allow those
individuals to learn these techniques and
eventually use them in their work
environment
(2) develop a system which is adaptable
in the sense that additional programs
could be incorporated into the system at
a later date without having to alter
previous programs or recompile the
entire system
(3) develop programs which produce
graphic output in a variety of forms and
of publishable quality to meet the needs
of research scientists and engineers
(4) include on-line help facilities and
extensive error checking in the programs
The on-line help facilities offer
information concerning the operation of
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the system, its capabilities and
limitations, how to alter the system, as
well as programming conventions and
definitions. GEOPACK allows the
incorporation of other programs, such as
the GEO-EAS (EPA/600/4-88/033)
system. Examples showing how this
software can be used in the analysis of
spatially correlated data can be found in
the GEOPACK users manual.
Basic System Description
The GEOPACK system includes
programs to do the more common
statistical and geostatistical analyses.
The system is estimation oriented in that
if the ordering in the menu system is
followed, a grid of estimates for the
selected variable in the data set will
result. A description" of the various
components of the system follows.
Baste Statistics
Basic statistics such as the mean,
median, variance, standard deviation,
skew, kurtosis and maximum and
minimum values can be determined for
the selected data set. Routines are also
available for linear regression, polynomial
• regression, Kolomogorov-Smirnov test for
distribution and calculating the
percentiles of the data set. A user-
supplied statistics package can be
incorporated into GEOPACK to allow the
user to access the comprehensive
statistical analyses that are contained in
many commercial statistics packages.
Var/ography
The sample semivariogram or cross-
semivariogram for a two-dimensional
spatially-dependent random function can
be determined. The approach used in
determining the sample semivariogram is
similar to that outlined in Journel and
Huijbregts (1978). A model can be fitted
to the sample semivariogram using the
nonlinear least-squares fitting procedure
of Marquardt (1963). This provides a first
estimate for the coefficients to be used in
a cross-validation program and helps to
automate the model-fitting procedure. If
the least-squares technique fails, or other
information is available which should be
included in the model-fitting process, the
traditional iterative method of selecting
the model coefficients and viewing a
graph comparing the sample values to
the model can be utilized.
Unear Estimation
GEOPACK includes programs to
calculate the ordinary kriging and
cokriging estimators in two dimensions
along with their associated estimation
variance. The programs include punctual
and block kriging and geometric
anisotropy. There is a cross-validation
option which uses the kriging estimator in
a jackknifing mode to cross validate the
spatial correlation structure. It is possible
to include indicator kriging in an analysis
by first transforming the data.
Nonlinear Estimation
Nonlinear estimators such as the
disjunctive kriging and cokriging
estimators can be determined along with
the estimation variance and the
conditional probability that the value is
greater than a specified cutoff level. Up
to 10 cutoff levels are allowed. As with
the linear estimation method, this type of
an analysis can be done on punctual or
block support and may include
anisotropy.
Help Facilities
The program includes on-line help
facilities to provide the user with
information concerning the operation of
the program, data requirements,
conventions, definitions, run-time errors,
missing files, etc. that are encountered
during execution. At the main menu level,
the help information is of a general
nature. During execution of a program,
the help is more specific, such as
defining a term. Virtually all the
information needed to operate or modify
the system is available from the HELP
facility.
Other Features of GEOPACK
The program also includes various
graphics capabilities such as linear or
logarithmic line plots, contour and pixel
diagrams. The program can be interfaced
with any user-supplied graphics package
so that custom diagrams can be_
developed.
GEOPACK uses dynamic allocation of
memory so that data sets with a wide
range of variables and positions can be
used without having to alter the program.
A large storage array is partitioned based
on the number of samples and variables
so that there is little wasted space
compared to defining the arrays to have a
fixed number. One limitation is that
GEOPACK allows a maximum of 10
variables plus their x and y positions and
a sample or position number. If an array
must be created by a program, the space
is obtained from the large storage array.
If attempts are made to use more
memory than is available, an error
message is printed out giving the
memory status. From this information, a
decision can be made on how to reduce
the memory needs to allowable limits.
GEOPACK uses data in a standard
ASCII format for data input. Data can be
entered with any program (data base or
spreadsheet) or word processor that
supports ASCII format. There is a seven
line header associated with each data file.
This header consists of three lines of title
information, the number of random
variables, total number of samples, the
names to use for the random variables,
and a format specifier which describes
the way the data is to be read into
GEOPACK. The format specifier follows
the ANSI FORTRAN convention. The
sample data file is on the following page.
Program Structure
The program' has been structured to
enable the addition of programs by end-
users. This has led to the development of
a menu system from which a particular
program is executed. Part of the system
is hard coded and cannot be changed;
but by using what is termed a USER'S
menu, a program or another user-defined
menu can be added to the system at any
time. The user menu is accessed from
the F5 key and reads the instructions
contained in a data file. The data file can
be modified to include a different set of
instructions, and thus allow the system to
be modified to suit the end-user's needs.
Through this menu, the end-user can add
any number of programs, menus and
subdirectories to the system.
Program Utilities
Many utility programs are included
enabling the user to access a variety of
information and other computer functions
while using GEOPACK. A sample of the
utilities from within GEOPACK are those
to 1) select, edit or modify an existing
data set^ 2) pack_the contents of the
temporary directory into a compressed"
format for later use or to extract all or
some of the files contained in a
compressed file, 3) display the program
structure, 4) temporarily leave the
program in a DOS shell, 5) execute a
DOS command, 6) view a file. Also
included are a number of utilities which
help the user to tailor GEOPACK to
specific needs by facilitating the passage
of information to the new user-supplied
applications.
Computer Requirements
The programs have been written in a
combination of FORTRAN and C
programming languages and run on IBM-
compatible microcomputers such as the
PC-AT, Compaq-286, -386, Zenith, etc.,
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This is a typical data file. There are 4 random variables: MOIST, TEMP, SAND and OIL-%. There are 119
positions where data was collected (only 4 positions are shown).
4 119
12 3546 7
MOIST
(G5.0.12F10.3)
1 6.0000
2 6.0000
TEMP
7.0000
10.0000
SAND
46.8500
46.2900
OIL-%
999.9990
5.9250
56.5102
55.6444
6.5362
5.2454
118
119
24.0000
22.0000
21.0000
24.0000
46.3500
47.1400
999.9990
999.9990
54.4012
52.5845
4.0463
2.5345
using an MS-DOS operating system
(ideally version 3.2 or greater) and 640 K
memory. (PC-XT and compatibles are not
recommended for GEOPACK.) A math
coprocessor is recommended but not
required. This is a mathematical intensive
system and calculations will be
significantly faster if a math coprocessor
is installed. The system can support the
use of a virtual disk (RAM disk) as the
tem'porary storage device. GEOPACK
also requires that the ANSI.SYS driver be
installed if the screen output is to perform
properly. Because of its integrated
nature, GEOPACK requires a hard disk
storage with about 4 Mbytes free disk
space. A graphics monitor is required
due to the graphical nature of the output.
GEOPACK supports either a CGA, EGA,
VGA or HERCULES graphics adapter and
the appropriate monochrome or color
monitor. The system includes a graphics
program for the printing of graphical
images and supports the following
devices: HPGL compatible plotters,
HPCL compatible printers, and Epson
compatible dot matrix printers.
Software Availability
The GEOPACK system in its
executable form is in the public domain
and can be obtained by sending four
Preformatted diskettes [either 5.25 inch
high density (1.2Mb) or 3.5 inch high
density (1.44Mb)] to:
GEOPACK Distribution
US EPA
Robert S. Kerr Environmental
Research Laboratory
P.O. Box 1198
Ada, OK 74821-1198
Telephone: (405) 332-8800
References
Journel, A. G., and Ch. J. Huijbregts,
Mining Geostatistics, Academic
Press, New York, 1978.
Marquardt, D. W., An Algorithm for Least-
squares Estimation of Non-linear
Parameters, J. Soc. Ind. Appl. Math.,
11:431-441, 1963.
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S. R Yates is with the U.S. Salinity Laboratory, Riverside, CA 92501 and M. V.
Yates is with the University of California, Riverside, CA 92521
David M. Walters is the EPA Project Officer (see below)..
The complete report, entitled "Geostatistics for Waste Management: A User's
Manual for the GEOPACK (Version 1.0) Geostatistical Software System,"
Order No. PB 90-186 4201 AS; Cost: $17.00 subject to change) will be
available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
Ada, OK 74820
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penally for Private Use S300
EPA/6QO/S8-90/004
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