c/EPA
United States
Environmental Protection
Agency
Robert S. Kerr Environmental
Research Laboratory
Ada, OK 74820
EPA/600/8-90/004
January 1990
Research and Development
Geostatistics for Waste
Management:
A User's Manual for the
GEOPACK (Version 1.0)
Geostatistical Software
System
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EPA/600/8-90/004
January, 1990
GEOSTATISTICS FOR WASTE MANAGEMENT:
A User's Manual For the GEOPACK (Version 1.0)
Geostatistical Software System
by
S.R. Yates
USDA/ARS
U.S. Salinity Laboratory
Riverside, CA 92501
and
M.V. Yates
Department of Soil and Environmental Sciences
University of California
Riverside, CA 92521
Interagency Agreement No. DW12932632
Project Officer
David M. Walters
Processes and Systems Research Division
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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DISCLAIMER
The information in this document has been funded wholly or in part by the United
States Environmental Protection Agency under interagency agreement No. DW-12932632
to the United States Department of Agriculture United States Salinity Laboratory.
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.
11
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FOREWORD
EPA is charged by Congress to protect the Nation's land, air and water systems.
Under a mandate of national environmental laws focused on air and water quality,
solid waste management and control of toxic substances, pesticides, noise, and
radiation, the agency strives to formulate and implement actions which lead to
a compatible balance between human activities and the ability of natural systems
to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of
expertise for investigation of the soil and subsurface environment. Personnel
at the laboratory are responsible for management of research programs to: (a)
determine the fate, transport and transformation rates of pollutants in the soil,
the unsaturated zone and the saturated zones of the subsurface environment; (b)
define the processes to be used in characterizing the soil and subsurface
environment as a receptor of pollutants; (c) develop techniques for predicting
the effect of. pollutants on ground water, soil, and indigenous organisms; (d)
define and demonstrate the applicability and limitations of using natural
processes, indigenous to the soil and subsurface environment, for the protection
of this resource.
This user's manual serves the purpose of instructing the user in the use of
GEOPACK, a comprehensive, user-friendly geostatistical software system. This
guide should help the end-user, both novice and sophisticated, to become familiar
with the features of GEOPACK. 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.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
111
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SUMMARY
A comprehensive, user-friendly geostatistical software system called GEOPACK
has been developed. The purpose of this software is to make available the
programs necessary to undertake a geostatistical analysis of spatially correlated
data. The programs were written so that they can be used by scientists, engineers
or regulators with little experience in geostatistical techniques and still
satisfy the requirements of more advanced users. Using these programs, and
spending a little time becoming familiar with geostatistics the end-user should
be able to include these techniques in their work and research environments.
Acknowledgements:
The research and development of the computer software described in this
report was supported in part by U.S. Environmental Protection Agency, R.S. Kerr
Environmental Research Laboratory, Ada, OK, 74820, through an interagency
agreement, no. DW-12932632. It has not been subject to the Agency's peer and
administrative review and therefore may not necessarily reflect the views of the
Agency, and no official endorsement should be inferred.
Disclaimer of Warranty
Although the authors of this software have endeavored to produce accurate,
reliable and correct software, this software (including instructions for its use)
is provided "as is" without warranty, expressed or implied. Furthermore, the
authors do not warrant, guarantee or make any representations regarding the use,
or the results of the use, of the software or written materials concerning the
software in terms of correctness, accuracy, reliability, currentness or otherwise.
The entire risk as to the results and performance of the software is the sole
responsibility of the user. if the software or written materials are defective,
the user and not the author, agents or employees assume the entire cost of all
necessary servicing, repair or correction.
Compaq'is a registered trademark of the Compaq Corporation. IBM*is a registered
trademark of the International Business Machines Inc. Microsoft" and MS-DOS* are
registered trademarks of the Microsoft Corporation. Hercules'is a registered
trademark of the Hercules Corporation. Zenith" is a registered trademark of the
Zenith Corporation. HP°, ThinkJet" and LaserJet" are registered trademarks of the
Hewlett Packard Company.
iv
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TABLE OF CONTENTS
Page
Foreword iii
Summary iv
Acknowledgements iv
List of Figures vi
Section
1 Introduction 1
2 Software Description and Operation Instructions
1. Computer Requirements ' 4
2. Installing GEOPACK
a. Installation instructions 4
b. Temporary storage directory , 5
c. Setting or changing the GEOPACK directory
specification 5
d. GEOPACK System Default Settings 5
3. System Overview
a. Program structure 6
b. Function keys and cursor movement 6
c. File-naming conventions 7
4. Data File
a. Format instructions 9
b. Examples of Data Sets 11
5. The Menu System
a. Description of the MAIN Menu 13
b. Description of the HELP Menu (Fl) 14
c. Description of the UTILITY Menu (F3) 15
d. Description of the VIEW Feature (F4) 18
e. Description of the USER Menu (F5) 18
f. Description of the Data Set Utility Menu 20
g. Description of the Statistics Menu 24
h. Description of the Variogram Menu , 26
i. Description of the Kriging Menu 32
j. Description of the Disjunctive Kriging Menu .... 35
k. Modifying and Adding Menus 36
1. Trouble-shooting 40
6. GEOPACK Enhancements
a. Running GEO-EAS geostatistics software 40
b. Description of GEOPACK utility programs 40
3 Examples
1. Virus Decay Rates In Tucson Ground Water 44
2. Salinity In a Southwest Arizona Field 54
3. Surface Moisture, Temperature and Texture 60
References and Suggested Literature 66
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LIST OF FIGURES
Figure 3.1.1. Example output from Variogram Calculation (Sample) program for the
data set, VIRUS.DAT. m A and B, respectively, are the tabular values and a plot
of the semivariogram function.
Figure 3.1.2. Example output from the Automatic Model Fit program. The solid
line is an spherical model that was fitted to the sample semivariogram.
Figure 3.1.3. Example output from Manual Model Fit, Select Model(s) program (in
A) and the Edit Variogram Model File (in B) .
Figure 3.1.4. Contour diagram of the estimated value of the decay rate using the
Ordinary [Co]Kriging and Line Contour Diagram programs is illustrated.
Figure 3.1.5. Contour diagram using the Ordinary [Co]Kriging and Block Contour
Diagram programs. In A and B, respectively, the estimated value for the decay
rate and the estimation variances are illustrated.
Figure 3.2.1. The semivariogram function for the natural logarithm of the
electrical conductivity using the Variogram Calculation (Sample) program and the
data set, ECSAR.DAT.
Figure 3.2.2. Contour diagram of the estimated value of the electrical
conductivity using the Disjunctive [Co]Kriging and Block Contour Diagram programs.
Figure 3.2.3. Contour diagram of the conditional probability that the estimated
value of the electrical conductivity is greater than the natural logarithm of 4
dS/m (i.e., 1.38 log{dS/m}) using the Disjunctive [Co]Kriging and Block Contour
Diagram programs. This figure shows the actual screen position of the contour
levels window when displayed.
Figure 3.3.1. The semivariogram function for the surface moisture content (in A)
and the surface soil temperature (in B) using the Variogram Calculation (Sample)
program and the data set, C912.DAT.
Figure 3.3.2. The cross-semivariogram function for the surface moisture content
and the surface soil temperature using the Variogram Calculation (Sample) program
and the data set, C912.DAT.
Figure 3.3.2. Contour diagram of the estimated value of the electrical
conductivity using the Ordinary [Co]Kriging and Block Contour Diagram programs.
Figure 3.3.3. Contour diagram of the estimation variance for electrical
conductivity using the Ordinary [Co]Kriging and Block Contour Diagram programs.
VI
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SECTION 1
INTRODUCTION
To use 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 someone is known 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 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 has been developed in cooperation with the U.S. EPA's R.S. Kerr
Environmental Research Laboratory, Ada, OK. It was developed with the philosophy
that geostatistical software is needed that can be used as a learning tool by
individuals with little or no geostatistical expertise and yet can also satisfy
the needs of individuals with more advanced training in geostatistical methods.
The specific objectives in creating GEOPACK were to develop: 1) geostatistical
software which is easy to use so that those with little training in geostatistical
methods can learn these techniques and eventually use them in their work
environment; 2) an integrated system which will free the user from excessive file
editing and program manipulation; 3) a system which is adaptable in the sense
that additional programs can be incorporated into the system by the end user at
a later date without having to alter previous programs or recompile the entire
system; 4) programs which produce graphic output in a variety of forms and of
publishable quality to meet the needs of research scientists and engineers and 4)
software which includes on-line help facilities and extensive error checking in
the programs. The on-line help facilities offer information concerning the
operation of the system, its capabilities and limitations, how to alter the system
as well as programming conventions and definitions.
GEOPACK allows the incorporation of other geostatistical programs, such as
GEO-EAS (reference), so the features of this and other programs can be accessed.
Examples showing how these geostatistical programs can be used in the analysis of
spatially correlated data can be found in Yates et al. (1986 a,b,c), Yates (1986),
Yates and Warrick (1987), Yates et al. (1988) and Yates and Yates (1988, 1989).
For individuals interested in learning geostatistical techniques, a number of
texts are available and include: Clark (1979), Journel and Huijbregts (1978),
Journel (1988) and David (1977) .
GEOPACK geostatistical software system is a package of programs for
conducting analyses of the spatial variability of one or more random functions.
The system is menu driven, and simplified so that a minimum number of input data
are needed. The programs also limit the amount of intermediate results printed
to the screen or the printer.
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.
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A large storage array (currently set to approximately 10000 storage locations) 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 of samples and
variable. One limitation is that GEOPACK allows data base (i.e. a data file) to
contain a maximum of 10 variables plus their x and y positions and a sample or
position number (the sample number must be a real number). During execution of
GEOPACK, whenever additional storage space (i.e. memory) is required 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
requirements to allowable limits (i.e. reducing the number of variables or samples
considered, etc.).
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.
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 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.
User-Defined Programs
GEOPACK includes a feature which makes it simple to access any user-defined
program (i.e. program not included with GEOPACK) for generating statistics, line
graphics, surface graphics, text editing and data base management systems. The
program names are defined in the GEOPACK System Default Settings file (see Section
2.5.c). Other miscellaneous user-defined programs can also be incorporated into
GEOPACK using the USER'S Menu (see Section 2.5.e).
Basic 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 base (i.e. a file containing one or more random functions plus their x and
y coordinates) . Programs are also included for linear regression, polynomial
regression, Kolomogorov-Smirnov test for distribution and calculating several
percentiles of a selected data set (i.e. for a particular random function such as
moisture content). GEOPACK can also directly access any commercially available
statistics package while running GEOPACK which allows the user to run more
comprehensive statistical analyses contained in a commercially available
statistics package.
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Variography
The sample semivariogram, the cross-semivariogram or a semivariogram for
combined random functions [i.e. , Z (x) + Y(x)] 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 Journal 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 auto-
mate 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 manually selecting the model coefficients and
viewing a graph comparing the sample values to the model can be used.
Linear Estimation
GEOPACK includes programs to calculate the ordinary kriging and cokriging
estimators in two dimensions along with their associated estimation variance.
Punctual and block kriging and geometric anisotropy are included. 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 creating an indicator variable using a data
transformation program supplied in GEOPACK.
Nonlinear Estimation
Nonlinear estimators such as the disjunctive kriging and disjunctive
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.
Graphics Outputs
Various graphics capabilities are included such as linear or logarithmic
line plots, contour and block (i.e. , pixel) diagrams. Device drivers for the HP*
Laser Jet® (series II), HP plotters, and dot matrix printers (similar to Epson"
printers) are included with GEOPACK. Drivers for other printers and plotters can
be written and included in GEOPACK. The graphics programs supplied with GEOPACK
produce intermediate quality output and are intended for quick and easy, albeit
rough, graphic illustrations. For the highest quality graphic output, GEOPACK can
be interfaced with any user-defined graphics package so that custom diagrams can
be developed. Using the USER'S Menu, any commercially available graphics packages
can be accessed while running GEOPACK. A particular data file can be plotted
using a commercial graphics package by either using an internal editor (if one is
included in the commercial graphics package) or by writing a simple format-
translation program to create a new output file in the correct format.
3
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SECTION 2
SOFTWARE DESCRIPTION AND OPERATION INSTRUCTIONS
2.1. COMPUTER REQUIREMENTS
GEOPACK has been written using a combination of Microsoft" FORTRAN and C
programming languages and runs on IBM°-compatible microcomputers such as the
PC-AT, Compaq"-286, -386, Zenith", etc. using an MS-DOS"operating system (ideally
version 3.30 or greater) and 640 K memory. GEOPACK does not require a math
coprocessor but will use one if it is available. A virtual disk can be used to
increase operating efficiency if it is defined to be the temporary storage
directory. GEOPACK also requires that the ANSI.SYS driver be installed for the
screen output to perform properly. GEOPACK requires hard disk storage of about
4 Mbytes and, either a CGA, EGA, VGA or Hercules" graphics adapter and the
appropriate monochrome or color monitor.
2.2. INSTALLING GEOPACK
2.2.a. Installation Instructions,
An installation program is supplied with GEOPACK to facilitate the
installation of GEOPACK onto a hard disk. To completely install GEOPACK, at least
4 Mbytes of free space must be available on the hard disk. The installation
program can be started by typing either
A: INSTALL destination drive and path>
or
A:INSTALL
If the optional and destination drive and path> are not specified,
the program will provide prompts for this information. The source drive can be
any legal floppy drive and the default value is A: . The destination drive and
path indicates the hard drive and subdirectory for the "root" of the
geostatistical programs. The default destination is C:\GEOPACK. It is advisable
to specify a destination drive and subdirectory since a number of programs are
copied to this subdirectory and could be accidentally deleted if only a drive
(i.e., C:) is specified, since typically root directories are used to store a
variety of programs. If any of these programs are deleted, GEOPACK may produce
unpredictable results.
Before GEOPACK will operate correctly, the computer must have a specific
configuration. To install GEOPACK, several modifications to the computer must be
made. These are described in more detail in the following sections.
1. A temporary storage directory must be created. This is done
automatically.
2. An environment variable must be set. The AUTOEXEC.BAT file must
be altered.
3. A system parameter file must be created. This is done automatically.
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You will need to modify this file (see Section 2.5.c) to add the
names of the editor, line and contour graphics, data base management
system, etc. you have available.
4e If you have a HERCULES graphics card, you must run MSHERC.COM
prior to starting a GEOPACK session. This program should be
put in the AUTOEXEC.BAT file.
5. The ANSI.SYS driver (see your MS-DOS manual) must be installed
in the CONFIG.SYS file. This is done by adding a statement
like: DEVICE=C: \DOS\ANSI. SYS to the CONFIG.SYS file. Be sure that
the correct path for ANSI.SYS is used.
2.2.b. Temporary Storage Directory.
GEOPACK uses a temporary storage directory to hold information such as the
data set, intermediate results, output files, etc. The installation procedure
automatically creates a temporary directory called TMP to be used to store
intermediate results. In general, the temporary storage directory is transparent
to the user.
2.2.c. Setting or Changing the GEOPACK Directory Specification.
GEOPACK will operate properly only if the environment variable %GEODIR% (the
"%" are used to indicate an environment variable) is set to the root of the
geostatistical programs. To set this variable the following line should be added
to the AUTOEXEC.BAT file
SET GEODIR=C:\GEOPACK
where C:\GEOPACK is the primary subdirectory for the geostatistical programs. In
the user-defined menus (described in Section 2.5.d) whenever GEOPACK sees
"%GEODIR%" it will substitute "C:\GEOPACK" so that a command: %GEODIR%\SHOWDIR
would be the same as C:\GEOPACK\SHOWDIR. Note, the above command can also be
typed at the MS-DOS prompt prior to starting GEOPACK. After typing the SET
command given above, if the DOS reply: "Out Of Environment Space" appears, the
user should consult the DOS manual about SHELL commands.
2.2.e. GEOPACK System Default Settings.
The installation program creates a file that contains the system default
settings. This file may require modification before all of the options on the
USER and other menus become active. Before making any modifications, see Section
2.5.C.
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2.3. SYSTEM OVERVIEW
2.3.a. Program Structure,
The initial program structure of GEOPACK is shown graphically as
GEOPACK
DKRG
KRIG
STAT
TMP
USER
VARI
DATA
- DSTAT
- GEOEAS
- UPROG
where , in the above example, the subdirectory GEOPACK is called the "root" of
geostatistical programs. The location of the "root" directory is specified during
installation and can be located on any fixed-disk drive and can be anywhere along
a subdirectory "tree". It is recommended that the root be the first level
subdirectory on a given drive.
The subdirectories: DKRG, KRIG, STAT, USER and VARI, respectively, are used
to store the programs for: disjunctive kriging and cokriging (DRKG), ordinary
kriging and cokriging (KRIG), basic statistics (STAT), user-defined programs
(USER) and variography (VARI). The menu entries for each set of analyses (except
for the USER menu) cannot be modified by the end-user. The TMP subdirectory is
created to be used as the temporary storage directory during installation.
The subdirectories of the USER directory: DATA, DSTAT, GEOEAS and UPROG are
examples of how GEOPACK can be altered to include additional programs. The menu
entries for the USER directory and its subdirectories can be modified by the
end-user to tailor GEOPACK for an individual's needs. The instructions required
to modify the GEOPACK USER menu are given in Section 2.5.k.
2.3.b. The Function Keys and Cursor Movement.
The function keys: Fl, F3, F4, and F5 can be used at any menu in the
following manner:
Fl - Help (At menu and program levels. In programs other F-keys
also display help information and are indicated when they
are active)
F3 - Utility Menu
F4 - View previous screen
F5 - User Menu (User-defined programs, menus etc.
Makes GEOPACK adaptable)
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A complete description of the entries on each of the menus that are accessed by
the Function keys is given in Section 2.5, The Menu System.
The cursor (i.e., the light bar or highlighted selection) can be moved by
using the following cursor control keys:
Home, End, PgUp, PgDn, Arrow Keys
If these keys are located on the keypad, the NUM-LOCK key must be turned off.
A menu entry can also be selected by pressing the letter (or number) that is
highlighted in the desired entry.
2.3.C. File-Naming Convention.
Whenever a data set is selected (this data set can be located in any
subdirectory on any disk) a file is created in the temporary storage directory and
is called "DEFAULT". This file contains two lines, the first gives the selected
file name and the second the origination path of the file. A copy of the selected
file is written to the temporary storage drive as well. These two files (DEFAULT
and the data set) are required before GEOPACK will run properly. All the programs
in GEOPACK read the DEFAULT file to obtain the name of the data set. The first
part of the data set name (i.e., "TEST" for a data set named "TEST.DAT") is used
for many of the intermediate file names. For a data set named "TEST.DAT" which
is assumed to contain three variables moist (variable #1) , temp (variable #2)
and sand (variable #3), the typical file names that reside in the temporary
storage directory and a brief description of their purpose follows.
STACKER.
MENUTEMP.BAT
DEFAULT.
TEST.DAT
RPLOT.TMP
GRAPH.DBF
TEST.V
- Used by the menu program.
- Used by the menu program.
Contains the name of the data set and path of
origination.
- Data set.
Basic descriptive statistics for all data
variables in the data set.
- Temporary file containing the data for the
last regression or least-squares graph.
A command file for the graphics program. Contains
the commands used to generate the last graph (regression,
least-squares, contour plot, etc.).
- The default settings file for the semivariogram
program. This file is generated when the Default
Settings program (on the variogram menu) is executed.
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VPLOT.DEF
VAR11.00
VAR11.01
VAR12.00
MVAR11.00
MVAR11.01
MVAR12.00
TEST.VAR
TEST.K
KPLOT.TMP
KPLOT1.TMP
TEST.D
TEST.DCi
DPLOT.TMP
DPLOT1.TMP
Temporary file containing the data for the
last semivariogram or cross-semivariogram graphed.
Contains the sample semivariogram values for
variable 1 (i.e., MOIST). First saved file.
Contains the sample semivariogram values for
variable 1 (i.e., MOIST). Second saved file.
Contains the sample cross-semivariogram values
for variable 1 with variable 2 (i.e., MOIST vs.
TEMP). First saved file.
Contains the model coefficients for the sample
semivariogram values contained in VAR11.00.
Contains the model coefficients for the sample
semivariogram values contained in VAR11.01.
Contains the model coefficients for the sample
cross-semivariogram contained in VAR12.00.
Contains the semivariogram and cross-variogram
coefficients for use by the kriging and dis-
junctive kriging programs.
The default settings file for the kriging program.
This file is generated when the Default Settings program
(on the kriging menu) is executed.
Contains the position, the estimate and the
estimation variance from the kriging program.
Temporary file containing the graphic data for
the last kriging contour graph produced.
The default settings file for the disjunctive kriging
program. This file is generated when the Default Settings
program (on the disjunctive kriging menu) is executed.
Contains the input data required by the dis-
junctive kriging program for variable "i", where
"i" is the variable number. This file is
created by executing the Hermite Coefficients
program on the disjunctive kriging menu.
Contains the position, the estimate, estimation
variance and conditional probabilities (if any)
from the disjunctive kriging program.
Temporary file containing a contour
representation of one of the output data
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types contained in DPLOT.TMP (i.e., it has the
last disjunctive kriging graph produced).
2.4. DATA FILE
2.4.a. Format Instructions.
To operate GEOPACK, a data file must be created in the proper format. Using
a text editor or word processor, a data file can be entered or modified for use
with GEOPACK. For GEOPACK to function properly, the data set must contain at
the minimum: 1) one (or more) spatially-dependent random variable(s) (i.e., soil
temperature, moisture, hydraulic conductivity, concentration, etc.) and 2) an
x and y position for each value of the random variable (s). A data file must be
created in ASCII format using the following standard FORTRAN formatting
instructions:
RECORDS 1-3:
RECORD
FORMAT(A7 6/A76/A76)
TITLE (3) Three lines of title.
FORMAT(2I5,F10.3)
IVAR The total number of random variables in
the data set. These are values of
the parameters that will be used in
obtaining estimates, etc.
NDAT The total number of positions (i.e.,
X and Y coordinate pairs) in the file.
CUTOFF The value given to this variable is the
maximum allowed value for the data. Using
the CUTOFF, missing data can be excluded
from any analysis. To accomplish this,
set any missing data in the data file to a
large number (e.g. 99999.99). This number
must be larger than the numeric value of
any variable. To exclude these large num-
bers , set the CUTOFF value to a number
slightly SMALLER than the missing data
number (e.g., 99999.00). Then the mis-
sing data will not be used by any program.
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RECORD
IINX
IX
IY
FORMAT(1315)
The column in the data file that contains
the sample number. if no sample is avail-
able, the program can be made to read a
blank field as zeros. In general, this
will not cause any problem in running the
programs.
The column in the data file that contains
the X coordinate data. See examples
given below for more information.
The column in the data file that contains
the Y coordinate data. See examples
given below for more information.
IV(1) The column in the data file that contains
one of the random variables. The sel-
ection of the first, second, etc. random
variable is arbitrary. The easiest way
to specify these is to sequentially num-
ber the random variables in the order
(from left to right) that they appear in
the data file. The program uses the order
you specify here, as the order the vari-
ables will be listed out on the screen.
If you want to change the order, then
give IV(1) as the 1st variable, IV(2) as
the second variable, and so on.
IV(IVAR) The column in the data file that contains
IVAR-th random variable.
RECORD
FORMAT(10(4x,A6))
NAM (I) The variable name for the I-th variable.
NOTE: the I-th variable is the variable
associated with IV(I) listed above. See
examples given below for more information.
10
-------
RECORD 7 :
FMT
RECORD 8-end:
DATA VALUES
FORMAT(A3 0)
Format specification for the data file.
This should be of appropriate form to
read the data in the file.
e.g.
(F5.0,2F10.3,5X,1E10.2)
(see RECORD 7)
The data set should have a sample number
(or index), X coordinates, Y coordinates
and the property(s) to be kriged. Data is
read until an end-of-file marker is found.
Therefore, there should not be any blank
lines in this part of the data file.
Note: The sample no. is assumed to be real.
2.4.b. Examples Of Data Sets.
This is a typical data file. There are 4 random variables: MOIST,
TEMP, SAND and OlL-%. There are 119 positions where data was col-
lected (only 4 positions are shown).
4 119
1235467
MOIST TEMP SAND OIL- %
(G5.0,12F10,3)
1 6.0000 7.0000 46.8500 999.9990 56.5102 6.5362
2 6.0000 10.0000 46.2900 5.9250 55.6444 5.2454
118 24.0000
119 22.0000
21.0000 46.3500 999.9990 54.4012 4.0463
24.0000 47.1400 999.9990 52.5845 2.5345
11
-------
Notes:
1) In the above example, the TEMP, MOIST, SAND and OIL are in columns 4,5,6
and 7, respectively. However, if you note line 5 and 6 you'll see that MOIST is
specified as variable #1, followed by TEMP, SAND and OIL. This changes the order
for the IV(i) and NAM(i) data.
2) Since all the random variables were not sampled at every location, some
method for delineating missing data is needed. In the above example, missing
data is specified by entering a large number (i.e., 999.9990). When executing a
program in GEOPACK, it will ask you the CUTOFF value (for delineating missing
data) and you should give a value slightly smaller than 999.9990 but larger than
any valid data value, for example, 999. or 900.
This example data file is the same as the one above except there are
no sample numbers. To alleviate this problem the first column of the
data file is specified as the sample number (i.e., they are all 0).
4 119
6 7
SAND oil-%
1235^
MOIST TEMP
(G1.0,F9.3,12F10.3)
6.0000 7.0000
6.0000 10.0000
46.8500 999.9990 56.5102 6.5362
46.2900 5.9250 55.6444 5.2454
22.0000
24.0000
47.1400 999.9990
52.5845
2.5345
12
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2.5. THE MENU SYSTEM
During installation, you are asked for the name you want to use to start the
geostatistical programs, where the default name is GEOPACK. After starting the
program using the selected name, the first menu displayed is the MAIN menu.
2.5.a. Description of the MAIN Menu.
Thu Jun 29, 1989 07:47:45 am
Return to MS-DOS, with prompt to save settings and files
GEOSTATISTICAL PROGRAMS: Main Menu
Quit GEOPACK
Data Set Utilities Menu
Statistics Menu
Variogram Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
Esc: quit
Fl: help
F3: util
F4 : view
F5: user menu
t
Home
End
From the main menu you can select one of several other menus using the cursor keys
to move the light bar (or highlighted region) over the desired selection or by
typing the highlighted character of the desired selection. The function keys will
display menus intended to offer help, utilities and user-defined applications.
Selecting an item from the MAIN menu will produce another menu containing programs
or other options which are available for undertaking the statistical and
geostatistical analyses. A description of the available menus follows.
When leaving GEOPACK (i.e., typing Q at the main menu) another menu is
produced which allows you to return to GEOPACK, return to MS-DOS leaving the
intermediate data in the temporary storage subdirectory, return to MS-DOS saving
the intermediate results to a packed file (see Section 2.5.f) or return to MS-
DOS and delete the intermediate results from the temporary subdirectory (see
Section 2.5.f) .
13
-------
2.5.b. Description of the HELP Menu (Fl) .
Return to Main Menu
Thu Jun 29, 1989 07:47:45 am
GEOSTATISTICAL PROGRAMS: Main Menu
Quit GEOPACK
Data Set Utilities Menu
Statistics Menu
Variogram Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
GEOPACK USER'S MANUAL
Return To Main Menu
Overview Of System
Installation Instructions
File Formatting Instructions
Basic System Operation
Menu Help
Utilities in GEOPACK
Adding User Programs and Menus
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
*
Home
End
If the Fl key is pressed from any menu, the HELP Menu is activated. On the
HELP Menu there are several help files you can access. In general, the
information in the User's Manual and some theory of geostatistics can be found on
the HELP menu.
14
-------
2.5. c. Description of the UTILITY Menu (F3).
Thu Jun 29, 1989 07:47:45 am
Return to Main Menu
GEOSTATISTICAL PROGRAMS: Main Menu
Quit GEOPACK
Data Set Utilities Menu
Statistics Menu
Variogram Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
Utilities Menu
Return To Main Menu
Change System Default Settings
DOS Shell
Execute an MS-DOS Command
Graph Most Recent Graphic
Program Structure
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
t
Home
End
If the F3 key is pressed from any menu, the UTILITY Menu is activated. On
the UTILITY Menu there are several programs available to alter basic GEOPACK
parameters, run MS-DOS commands while inside GEOPACK and view the current GEOPACK
program structure. Each utility is described in more detail below.
Change System Default Settings:
This Utility allows you to change the default settings which are used by
GEOPACK. The default settings include the path specifications, device names,
screen type, default colors and names of default (i.e., user defined) programs.
Two files are used: SYSETUP and SYSDEFLT for changing and storing the system
default information. SYSETUP is the basic file which MUST be present in the
GEOPACK root directory. This file contains the information which is written to
the screen by this Utility program, an example is:
15
-------
System Default Settings File
RAM-Disk or Temporary Directory
Data Storage Directory
Text Color Number (0-15)
Border Color Number (0-15)
Screen Mode (0=Black & White, l=Color)
Statistics Program
Word Processor or Text Editor
Line-Type Graphics Program
Contouring Graphics Program
Data Base Management Program
C:\GEOPACK\TMP
C:\GEOPACK\USER\DATA
11
6
1
MICROSTAT
EOT
GRAPHER
SURFER
MFOXPLUS
Esc: quit
Fl: help
F2: save
Home
End
Page Up
Page Down
Since paths are not given for any of the Default programs, it is required that
these programs reside in sub-directories on the current MS-DOS PATH (so that they
can be found from any sub-directory by using the program name only). It is also
possible to specify the entire MS-DOS path and program name. PLEASE NOTE: the
programs MICROSTAT, EDT, GRAPHER, SURFER and MFOXPLUS are commercially available
programs and are not included with the GEOPACK system. The Utility program writes
out a file (called SYSDEFLT which is used by the GEOPACK programs. An example of
this file is:
Columns :
C:\GEOPACK\TMP
C : \GEOPACK\USER\DATA
11
C
b
i
MICROSTAT
EDT
GRAPHER
SURFER
MFOXPLUS
1 1
1 10
1
20
This file is used by GEOPACK during operation of the programs. At any time if
there is a change in the definition of any item in SYSDEFLT a change needs to
be made to this file. The easiest way to do so is to use the Change System
Default Settings option on the Utilities Menu (i.e., F3 key).
16
-------
To manually run the Default Settings program type: DEFLT sysetup sysdeflt
from the root directory of GEOPACK. This may be necessary if the sysdeflt file
is ever accidentally deleted or modified.
DOS Shell:
This Utility allows you to temporarily exit the GEOPACK system and return
to the MS-DOS command-line mode. When you exit to a DOS shell, the text color on
the screen will be red. This is to remind you that you are in a DOS shell. Once
you are finished running MS-DOS commands you can return to GEOPACK by typing EXIT,
which exits you from the DOS Shell.
Please Note: While in a DOS shell, some of the available computer memory is
still allocated to GEOPACK and if you try to run a program that requires a lot of
memory you may see the message "not enough memory". If you must run this program,
you should exit the DOS shell (i.e., return to GEOPACK) then exit GEOPACK. This
will free up all the available computer memory. Also, it is possible to exit to
a DOS shell and restart GEOPACK (this can be done several times). If this is
done, the computer may stop operating since there is insufficient memory to
contain both the current and pre-installed versions of GEOPACK.
Execute an MS-DOS Command:
This Utility is similar to DOS Shell except that it allows you to run ONE
MS-DOS command. Once you have run the MS-DOS command you are returned to the
Utility Menu. If you need to run several MS-DOS commands, it is more efficient
to exit to a DOS shell.
Please Note: There is slightly LESS available computer memory when Executing
an MS-DOS command compared to exiting to a DOS shell.
Graph Most Recent Graphic:
This convenience feature allows you to replot the last graph displayed (or
that should have been displayed) on the screen. This feature is useful for
computers with insufficient memory to display graphs while in an application
program (i.e. the computer doesn't have enough extra memory to run the graphics
program). Use this options if you don't see a graph and receive the error
message: OUT OF MEMORY.
Program Structure:
This Utility gives a pictorial representation of the current GEOPACK
structure (for an example see Section 2.3.a). Changes in the structure of GEOPACK
will be reflected in the diagram produced by this program. The USER menu,
described in Section 2.5.d, can be modified to include any program, or add another
menu. In the above example, the USER menu is used to access four other menus,
17
-------
DATA, DSTAT, GEOEAS and PROG. These menus are for, respectively, available data
sets, default statistics program, GEO-EAS geostatistical software and user-defined
programs. Additional menus and programs can be added by following the instruc-
tions on modifying the USER MENU given in Section 2.5.J.
2.5.d. Description of the View Feature. (F4)
If for some reason you are located at one of the menus and you need to see
the last screen of output from a program that has just been completed, you can
toggle between the menu screen and the program screen by typing F4 provided your
monitor and graphics card allows multiple screens.
2.5.e. Description of the USER Menu. (F5)
Return to Main Menu
Thu Jun 29, 1989 07:47:45 am
GEOSTATISTICAL PROGRAMS: Main Menu
Quit GEOPACK
Data Set Utilities Menu
Statistics Menu
Variogram Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
User Menu
Return To Main Menu
EPA GEO-EAS
Graphics Menu
Statistics Package (Default)
Data Base Management (Default)
User Programs
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
t
Home
End
If the F5 key is pressed from any menu, the USER'S Menu is activated. The
USER'S Menu allows GEOPACK to be modified to include other programs and menus
which are defined by the user. The instructions which tell GEOPACK which program
to run or menu to display are in a file called: USER.MEN, which is located in the
root directory of the geostatistical programs (i.e. , if the default directory was
chosen, it would be C:\GEOPACK). The necessary information for modifying the
GEOPACK program is given under the heading "Adding User Defined Programs and
Menus" on the User's Manual Help screen (i.e. , type Fl) .
18
-------
A brief description of the menu options which are provided with the original
GEOPACK system follows.
Statistics Package (Default):
This feature allows you to run a default statistics package during a GEOPACK
session. The default statistics package is defined (i.e., the path and name
specified by using the system default setting program). To start this program
type F3 and select "Change System Default Settings". In the present example, it
is assumed that the GEOPACK data set will have to be modified to a format that the
default statistics package can read. Therefore, selecting this option will
produce another menu which will let you create a file in the proper format (Note:
this program may have to be changed for other statistics programs) and run the
statistic program. The default statistics menu is located in the subdirectory:
%GEODIR%\USER\DSTAT under the file name: DSTAT.MEN.
Graphics Menu:
This feature allows you to run one of several graphics programs during a
GEOPACK session. When this option is selected another menu is produced which has
three options. The first is to execute the GEOPACK graphics program and the other
two are the default line and contour graphics programs.
Data Base Management System (Default):
This feature allows you to run a default data base management system during
a GEOPACK session.
GEO-EAS:
This feature allows you to run GEO-EAS during a GEOPACK session.
Available Data Sets:
This option allows you to select a data set from a subdirectory used solely
for storing data sets. The subdirectory specification is %GEODIR%\USER\DATA and
the program SDATA.EXE is used for displaying and selecting the data sets located
in the directory (for additional information see Select a Data Set in Section
2.5.f) .
19
-------
2.5.f. Description of the Data Set Utilities Menu.
Return To Main Menu
Thu Jun 29, 1989 07:47:45 am
GEOSTATISTICAL PROGRAMS: Main Menu
Data Set Utilities Menu
Q - Return To Main Menu
Select a Data Set
Modify an Existing Data Set
Pack Temporary Directory into File
Unpack Temporary Directory from File
Extract a File From a Packed File
List Temporary Directory and View File
Edit a Data Set
Delete All Files in Temporary Directory
Esc: quit
Fl: help
F3: util
F4 : view
F5: user menu
t
Home
End
If the highlighted key "U" is typed or the light bar placed over the menu
option "Data Set Utilities Menu" on the MAIN Menu and the enter key pressed, the
Data Set Utilities Menu is' activated. On this menu there are several utilities
which can be used to select, edit or modify an existing data set, to pack the
contents of the temporary directory into an ARCHIVE file for later use or to
extract all or part of the files from the archive.
Select a Data Set:
This program allows the selection of an existing data set. The data set
must be properly formatted for use with GEOPACK. To create a new file, see the
editing program described below.
20
-------
Select a Data File
C:\GEOPACK\USER\DATA\..
.A
C912.DAT
ECSAR.DAT
TEST.DAT
VIRUS.DAT
ESC: exit
Fl: help
F2: list
Pg Up
Pg Down
Home
End
A data set can be selected by either 1) typing in the file name or 2) by
moving the light bar over the desired data set and typing the ENTER key. Other
subdirectories can be accessed in a similar manner to data files. Please note
that the symbol ..\ above indicates the subdirectory C:\GEOPACK\USER and if a
directory entry is preceeded by a "\", then the entry is a directory
specification.
This program copies the requested data from its current path to the
temporary directory, creates a file called DEFAULT which contains the program name
and its origination path. GEOPACK uses the DEFAULT file to determine the proper
name of the data file. Both files (i.e, the data file and DEFAULT) must exist on
the temporary directory before GEOPACK will work properly.
GEOPACK requires that a cutoff value be supplied during execution of the
programs. The cutoff value is used to indicate missing data. The cutoff value
is a specified value that is larger than any of the "true" data in the data set.
For example, if you have a variable that is missing a value at a point in
space, in the data set you place a value which is larger than any of the "true"
data and larger than the cutoff value which you must specify. During execution
of a program you will give a value (called the cutoff value) which is used by the
program to determine which values to ignore. Any value in the data set that is
greater than the cutoff value will be ignored by the program. It is imperative
that the cutoff value you specify is appropriate for given data set; if not, the
resulting calculations will be inaccurate.
21
-------
For example: given the following data:
index x y variable 1 variable 2 variable 3
3 10.0 11.2 12.55 45.66 1002.321
15 14.9 1.9 11.83 48.19 1032.209
5 18.7 7.7 12.91 36.98 1200.500
7 5.2 14.5 9.50 9999.99 1002.321
45 46.4 16.4 16.82 45.66 1002.321
the value used to indicate missing data is 9999.99. Note that this value is
greater than any value of ALL the variables. An appropriate cutoff value to
input into GEOPACK would be greater than 2000, since 1200.5 is the largest "true"
data value.
Modify an Existing Data Set:
This program allows the creation of new variables in an existing data set.
The data set must reside on the temporary directory prior to starting this program
and be properly formatted for use with GEOPACK. The newly created variables can
be added to the file. For example, assume the data set has one variable called
the moisture content. If a new variable log(moisture content) is to be created
it can be added to the file.
Pack Temporary Directory into File:
This program allows the archiving of the files residing in the temporary
directory. This is used if you want to store the intermediate results from
GEOPACK for use at a later time. Each file is "PACKED" into a new file in the
selected directory under a name you provide. If a file with the same name exists,
you will be asked if you want to overwrite it. The screen is similar to the
screen shown in the section "Select A Data Set" described above.
Unpack Temporary Directory from File:
This program allows you to retrieve the files that were previously packed
using the program described above. If you want to retrieve only a few of the
files then use the program described below under EXTRACT A FILE. The screen is
similar to the screen shown in the section "Select A Data Set" described above.
Extract a File From a Packed File:
This program allows you to retrieve one or more of the files that were
previously packed using the PACK program described above. Please note that you
must retrieve the DEFAULT file if you plan to use GEOPACK. If you fail to do so
the program will print an error message alerting you to this error (the program
does not explicitly state that the DEFAULT file is-missing, however) . The screen
is similar to the screen shown in the section "Select A Data Set" described above.
22
-------
List Temporary Directory and View File:
This program allows you to list all the files that currently reside in the
temporary directory. To "VIEW" a file place the light bar on the desired file and
type return. Also, by typing the F2 key, additional information about the file
is available. The screen is similar to the screen shown in the section "Select
A Data Set" described above.
Edit a Data Set:
This program allows you to edit a file. Any file can be edited whether it
exists or not. Once this program is started, you will see the directory listing
of the %GEODIR% directory (i.e. , the root of the geostatistical programs) and you
can select a file from this directory, supply an alternate file (and path) or
give a new directory name to see the listing of the new directory.
Remove All Files in Temporary Directory:
This command allows you to remove all the files in the temporary
directory. PLEASE NOTE: THE TEMPORARY DIRECTORY SHOULD BE USED ONLY FOR THE
GEOSTATISTICAL PROGRAMS SINCE THIS COMMAND WILL REMOVE ALL PROGRAMS IN THIS
DIRECTORY (or subdirectory).
Before you can select a second data set to work on, the temporary directory
must be cleared of a previous data set. If you want to save the intermediate or
final results from this previous data set, use the PACK data set program described
above.
23
-------
2.5.g. Description of the Statistics Menu.
^^^^^^=^^^^^^= Thu Jun 29, 1989 07:47:45 am
Return To Main Menu
GEOSTATISTICAL PROGRAMS: Main Menu
Statistics Menu
Return To Main Menu
Sample Statistics
Regression Analysis
Kolomogorov Test of Distribution
Least Squares Polynomial
Percentiles of Data
Variogram Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
t
Home
End
If the highlighted key "S" is typed or the light bar placed over the menu
option "Statistics Menu" on the MAIN Menu and the enter key pressed, the
Statistics Menu is activated. On the Statistics Menu there are several programs
from which you can choose. These programs are intended to do the most basic
statistical analyses and are not intended to replace comprehensive statistical
packages which are available commercially. Since it is anticipated that there will
be a need for accessing a more complete statistical package, GEOPACK has built in
capabilities to call (i.e., run) a user-defined statistical program from the
USER'S MENU (access to the USER'S MENU is obtained by typing F5). Since the data
format requirements of GEOPACK may be different from the commercial statistics
package, an interface maybe necessary to rewrite the data file in the appropriate
format. When this is necessary, it is advisable to have the Default Statistic
Package option on the USER menu call up another menu which has the interface and
start commands on it. An example is provided in the file %GEODIR%\USER.MEN.
Sample Statistics:
This program calculates the descriptive statistics for the data set. These
statistics include: the number of samples used, the mean, median, variance,
standard deviation, skew, kurtosis, maximum and minimum values of the data set.
24
-------
Regression Analysis:
This program calculates the linear regression coefficients, A and B, for the
linear model
variable (i) = A + B*variable(j), j * i
A plot of the data and regression line is provided as well as the coefficient of
determination, and a comparison between the estimates and data values.
Kolomogorov Test of Distribution:
This program calculates the Kolomogorov-Smirnov test statistic for a normal
distribution. Other distributions can be tested for by transforming the variable
of interest using the Modify a Data Set command on the DATA SET UTILITIES MENU.
Least Squares Polynomial:
This program calculates the nonlinear regression coefficients C(i) for the
polynomial model
variable(i) = C(l) + C(2)xvariable(j) + C(3)xvariable(j)z + ...
A plot of the data and regression line is provided as well as a comparison between
the estimates and data values,
Percentiles of Data:
This program sorts the data set and gives several pre-defined percentiles
of the data.
25
-------
2.5.h. Description of the Variogram Menu.
= Thu Jun 29, 1989 07:47:45 am
Return To Main Menu
GEOSTATISTICAL PROGRAMS: Main Menu
Variogram Menu
Return To Main Menu
Set Program Parameters
Variogram Calculation (Sample)
Automatic Model Fit
Manual Model Fit, Select Model(s)
Edit Variogram Model File
Statistics Menu
Ordinary [Co]Kriging Menu
Disjunctive [Co]Kriging Menu
Esc: quit
Fl: help
F3: Util
F4 : view
F5 : user menu
t
Home
End
If the highlighted key "V" is typed or the light bar placed over the menu
option "Variogram Menu" on the MAIN Menu and the enter key pressed, the Variogram
Menu is activated. The programs on the Variogram Menu are intended to do the
variogram analyses and should include the programming needed in the majority of
cases. Using the F5 key and interfacing to GEO-EAS allows YOU to use the
variogram program included in GEO-EAS. In some cases the GEO-EAS program may
include some feature not found in GEOPACK so it is advisable to check GEO-EAS if
you want a feature not currently supported in GEOPACK. Since the data format
requirements of GEOPACK are different from GEO-EAS, an interface is necessary and
has been written into the GEOPACK system. You must remember the names you give
to various files while running GEO-EAS since it doesn't have a specified naming
convention. When GEOPACK writes a file which is in GEO-EAS format it always has
the extension EPA (i.e., .EPA).
GEOPACK will save up to 15 sample semivariograms using the following naming
convention:
\VARij.00
first saved sample semivariogram
for variable i with j (i, j = l,..,IVAR)
if variable 1 is MOIST, 2 is TEMP
and 3 is SAND, then if 1=1 and j=2
VARij.OO is the first cross-variogram
between MOIST and TEMP saved by
GEOPACK.
26
-------
\VARij.01
CRAM drive>\VARij.02
. .03
second saved sample semivariogram
third saved sample semivariogram
\VARij.14
fifteenth saved sample semivariogram
Set Program Parameters:
GEOPACK provides you with a program for setting the variogram parameters to
facilitate using GEOPACK in an efficient manner. This program allows you to
specify a value for any of the parameters used to calculate the sample semi-
variogram or cross-semivariogram. You can specify any or all of these parameters
and once they are specified, the program will not ask for interactive input during
execution. For example, if you want to run the program five times and are
planning to change only one parameter each time, you would give a "?" in the
parameter field for that parameter. During execution you will be asked to
provide only that value. In this manner, you will only have to answer the
necessary questions during execution.
Spatial Correlation Function
Parameter Settings File
Data File Name: (FNAME)
Enable Graphics Options (i.e., -G) (Y/N )
Save All Sample Variogram Functions (Y/N )
Data Cutoff Value: (CUTOFF)
Number of Lagged Distances
Distance Between Lagged Distances:
Width of Lagged Interval:
Width of Angle Class:
Number of Directions:
Angle for Direction Number-1
Angle for Direction Number-2
Angle for Direction Number-3
Angle for Direction Number-4
t up 4- down Home PgUp PC
( NLAG )
( BLAG )
(WLAG)
( DALF )
( NDIR )
;Dn End F2=Save
TEST. DAT
Y
Y
100.0
12
1
0.0
90.0
1
0.0
30.0
60.0
90.0
Esc=Exit
27
-------
Variogram Calculation (Sample):
This program calculates the sample semivariogram or cross-semivariogram for
a spatially-dependent, two-dimensional random function.
There are two ways that the results from the sample semivariogram program
can be saved. The easiest method is to specify in the Parameter Settings file to
save all sample semivariograms (i.e. , Place a "Y" in the appropriate field) .
When this is done, every time the sample semivariogram program is run, the
results will be stored on the temporary subdirectory. Since 15 files may be saved
at any time, you will most likely never run the program more than 15 times so
saving every file will not produce a problem. If you should create 15 files and
wish to save additional sample semivariograms, you can delete files that you do
not expect to use.
An alternative method for saving the output from the semivariogram program
is to save the output from only those runs that produce "reasonable" results.
This can be done by selecting OPTION KEY: "S" at the end of the Sample Variogram
Calculation program. The OPTION KEYS appear at the lower right hand corner of
the screen during execution of a program. The "S" option only appears at (or
near) the end of the program and generally after a graphic plot of the sample
semivariogram has been produced.
Fit Model Automatically To Sample Variogram:
This program allows you to fit a mathematical model (e.g., a gaussian,
exponential, linear, spherical or power model) to a sample semivariogram. The
fitting method uses the nonlinear least squares minimization technique of
Marquardt (1963).
Sample Autocorrelation Functions Saved
MOIST / MOIST
MOIST / TEMP
MOIST / SAND
TEMP / TEMP
TEMP / SAND
SAND / SAND
00 01 02 03 04
00 01
00
Fl: view Enter: select
D: delete
Home End Pg Up
Pg Dn
28
-------
To specify a sample semivariogram (first step in running this program),
a screen is produced which shows all the saved variograms for each random function
and all the cross-variograms for each pair of random functions. This screen
displays the random function name, such as:
MOIST / MOIST
MOIST / TEMP
for a direct semivariogram for MOIST
for a cross-semivariogram for MOIST and
TEMP
followed by a series of numbers, such as
MOIST / MOIST
MOIST / TEMP
00 01 02 03
00 03
The numbers indicate the 00th (or Olth, etc.) saved sample semivariogram for the
specified random function(s). Given in Section 2.3 is a description of the naming
convention used by GEOPACK. The numbers (i.e. , 00 or 01, etc.) are the extension
of the sample semivariogram file name (i.e., VARij.OO).
Typing RETURN selects the particular sample semivariogram file for use by
the fitting program. Typing Fl gives some information about the sample semi-
variogram file that the cursor is highlighting. This help information is supplied
to help you determine which file you want to use when you have a number of files
from which to choose. The output from the fitting program is stored on the
temporary drive (or subdirectory) using a naming convention similar to the sample
semivariograms. After a sample semivariogram has been modeled (and the results
saved -- SEE SECTION ABOVE ON SAVING THE SAMPLE SEMIVARIOGRAM) the model
coefficients are saved in a file
\mVARij.00
\mVARij.01
\mVARij.02
first saved semivariogram model
coefficient file. This file corresponds to
\VARij .00
second file saved
third file saved
\mVARij.14
fifteenth file saved where the "m" is used to
designate the MODEL semivariogram file.
29
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Save Model(s). Fit Model Manually:
This program displays the model semivariogram coefficients that have been
modeled using the automatic fitting program and allows the user to select the
"best" model to be saved in a file for use by the kriging program. The program
allows you to save, view and manually model the semivariogram. Each operation is
described below.
Saving a Semivariogram. The semivariogram model can be saved to the file
which then becomes available to the Ordinary [Co] kriging and Disjunctive
[Co]kriging programs. This must be done prior to kriging, otherwise the kriging
program will not have a variogram model to use in the calculations. If the
semivariogram models were fitted to the sample semivariogram using the
"least-square" method (i.e., automatic fitting procedure), then the semivariogram
model should be cross-validated prior to kriging. To do this, use the Cross
Validation option on the Ordinary [Co]Kriging menu. To save the a semivariogram:
type "S", "RETURN" and give the line number of the model you want saved. If no
semivariogram model coefficients are saved, the kriging program will not work
properly and an error message will be printed out stating that no semivariogram
model coefficients were found.
Viewing a Semivariogram. This option allows you to view a saved
semivariogram. You might want to do this if you have saved many semivariograms
and are trying to determine the one you want to use for kriging.
To view the a semivariogram: TYPE "V", "RETURN" and give the line number of
the model you want plotted. If you want to view several semivariogram then give
the line numbers using the format: "1,2,3" for lines 1 to 3. Note, you can only
view 3 or less models on one graph.
Manually Modeling a Semivariogram. This option allows you to alter the
coefficients of a saved semivariogram. You must use the automatic fitting program
prior to manually modeling a semivariogram since this gives you a good starting
point for the coefficients. If several model files are available, you can see the
sample semivariogram from which the model was derived by typing the Fl key.
If you choose to manually model the semivariogram, you MUST place the model
coefficients into the variogram model file manually, as well (unless you decide
to use the automatically fitted values listed on the screen).
To manually model a semivariogram: TYPE "M", "RETURN", change the
coefficients shown at the bottom of the screen, and type "ESC" to have the model
and sample semivariograms plotted.
30
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Edit Variogram Model File:
This program allows the user to directly edit the file which stores the
models for the semivariogram. If a model is fitted to a sample semivariogram
manually, then the model coefficients must be manually entered into the variogram
model file using this program.
Variogram Editor: File: G:\TEST.VAR
. . _
-U
— Variables Model Nugget Sili-JMuggec Kange ^ —
MOIST / MOIST : Exponential o
MOIST / TEMP : Exponential o
MOIST / SAND None 0
TEMP / MOIST Exponential o
TEMP / TEMP Exponential 2.001
TEMP / SAND None 0
SAND / TEMP None 0
SAND / SAND None 0
Esc: Exit Fl: Help F2 : Save <- t -» Home
1.371 8.001 00
-2.999 9.994 00
0 0 00
-2.999 9.994 00
15.003 4.513 00
0 0 00
0 0 00
0 0 00
End Page Up Page Down
If no semivariogram model coefficients are saved, the kriging program will
not work properly and an error message will be printed out stating that no
semivariogram model coefficients were found. To correct this error, use the Save
Model(s), Fit Model Manually program to save the semivariogram model coefficients
for the random functions of interest.
31
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2.5.1. Description of the Kriging Menu.
Return To Main Menu
Thu Jun 29, 1989 07:47:45 am
GEOSTATISTICAL PROGRAMS: Main Menu
Ordinary [Co]Kriging Menu
Return To Main Menu
Set Program Parameters
Cross Validation
Ordinary [Co]Kriging
Line Contour Diagram
Block Contour Diagram
Statistics Menu
Variogram Menu
Disjunctive [Co]Kriging Menu
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
*
Home
End
If the highlighted key "0" is typed or the light bar placed over the menu
option "Ordinary [Co] Kriging Menu" on the MAIN Menu and the enter key pressed, the
Kriging Menu is activated giving access to several programs for calculating
estimates of the selected random function(s) in space. You can use the F5 key to
interface to GEO-EAS (or other programs) which allows you to use the ordinary
kriging program for one random function included in GEO-EAS.
Set Program Parameters:
Information on using the setting of the program parameters for kriging is
similar to that given in Section 2.5.1. An example of the screen generated by the
Set Program Parameters program is given below. More information about the
parameters can be found by starting this program and using the Fl key.
32
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Kriging Parameter Settings File
Est LOG in File
(Y/N) :
Maximum Search Radius:
Contour File:
(Y/N)
Enable Graphic Option:
ESTIMATE GRID: (P/B)
No. of Points
No. of Points
No. OF VARIABLES
Estimate Var
Auxiliary Var
Auxiliary Var
Auxiliary Var
Auxiliary Var
- X
- Y
n
#i
#2
#3
#4
N
20.00
Y
Y
P
30
30
?
1
2
3
?
?
BLOCK KRIGING DISCRETIZATION
No. of Cells -
No. of Cells -
«-left right->
X
Y
t up 4-dc
3
3
>wn Home
Anisotropy Ratio:
Anisotropy Angle:
Number Contour Levels:
Save Intermed. Results
ORIGIN
Width Betw. Pts - X
Width Betw. Pts - Y
No. NEAREST NEIGHBORS
Estimate Var #1
Auxiliary Var #1
Auxiliary Var #2
Auxiliary Var #3
Auxiliary Var #4
BLK COVAR. (0 default)
Width of Cell - X
Width of Cell - Y
PgUp PgDn End F2 =
1.0
0.0
4
N
0.0,0.0
?
?
10
10
10
10
10
0.0
?
?
Sav Esc=Exit
Cross-validation:
GEOPACK provides you with a program that allows you to cross-validate the
model for the spatial correlation structure. The cross-validation technique used
is a semi-quantitative technique based on kriging and is used to evaluate whether
the covariance function (or variogram) is appropriate for the experimental data.
The method involves estimating the value of the random function of interest at
every known sampling location but excluding the known value from the estimation
process (the known value is excluded because kriging is an exact interpolator).
Using all the pairs of actual and estimated values, various quantities can be
calculated and used as an indication of the "quality" of the model spatial
correlation function.
Ordinary Kriging and Cokriging:
The program GEOKRIG is used for kriging and cokriging. GEOPACK allows up
to 10 variables to be used for cokriging although it is advisable to use 4 or
less random functions in practice. If more than 5 random functions are used, the
default settings program cannot be used while running the kriging program, since
it only allows you to input 1 primary and 4 auxiliary random functions. A large
static array of 10000 words is partitioned for storage of input data, the kriging
matrix, etc. so there is a limit to the size of problem that can be executed with
this program.
33
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GEOPACK allows you to create estimated values in one of two manners, either
on a grid system or by reading a file of x and y coordinates. This latter method
is useful if irregularly spaced estimates are required.
Estimates on a Grid. The first method is to create a grid system with
estimated values and estimation variances at each of the nodal points. To do
this, you must supply the following information:
1. The origin of the grid system (usually the origin for
the collected data is used).
2. The number of columns of estimates in the X direction
3. The distance between columns in the X direction
4. The number of rows of estimates in the Y direction
5. The distance between rows in the Y direction
For this case, the total number of estimates is (Number of columns)-(Number of
rows).
Read Locations From a File. An alternative method for determining the
placement for calculating estimates is to create a file which contains a list of
the desired X and Y coordinates for the placement of the estimates. When using
this option, GEOPACK will prompt you for the file name and use the file to
determine the placement of estimates.
Line Contour Diagram:
A contouring package is provided with GEOPACK so that the output files from
the kriging program can be graphically illustrated. The output file from the
kriging program is in the temporary storage directory with a name: KPLOT.TMP. The
contouring program reads this file and produces an output file KPLOT1.TMP which
can be used by the graphics program to draw a contour plot on any device for which
a device driver is supplied.
Block Contour Diagram:
The pixel contour program is similar to the line contouring program
described above except that the estimation grid is presented on the screen and
each cell is filled with a color and/or pattern in correspondence to the estimated
value of the particular cell. This provides another method for viewing the
results of the data and gives a better feel of the coarseness of the grid system.
The pixel diagram which results from using this program can be printed by using
the GRAPHICS.COM utility supplied with MS-DOS and the PRINT-SCREEN key.
34
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2.5.J. Description of the Disjunctive Kriging Menu.
Thu Jun 29, 1989 07:47:45 am
Return To Main Menu
GEOSTATISTICAL PROGRAMS: Main Menu
Disjunctive [Co]Kriging Menu
Return To Main Menu
Set Program Parameters
Hermite Coefficients (DK Step 1)
Estimates, [Co] Kriging (DK Step 2)
Line Contour Diagram
Block Contour Diagram
Statistics Menu
Variogram Menu
Ordinary [Co]Kriging Menu
Esc: quit
Fl: help
F3: Util
F4 : view
F5: user menu
t
Home
End
If the highlighted key "D" is typed or the light bar placed over the menu
option "Disjunctive Kriging Menu" on the MAIN Menu and the enter key pressed, the
Disjunctive Kriging Menu is activated giving access to several programs for
calculating estimates and conditional probabilities of the selected random func-
tion (s) in space.
Set Program Parameters:
Information on the setting of program parameters for disjunctive kriging can
be found in Sections 2.5.h and 2.5.1 (i.e., variograms and kriging). One
difference between this program and the previous programs is that there are two
screens of parameters that can be set for disjunctive kriging. To toggle to the
next screen type Ins.
Calculate Hermite Coefficients:
The first step in disjunctive kriging is the definition of a transform
variable. The transform variable is assumed to be hi-variate normally dis-
tributed. The program calculates the transformed values of the data set which are
35
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used in the disjunctive [co]kriging program. For each random function that will
be used for kriging, a transformed data set must be calculated (i.e. , run this
program for each data set selected). As a check on the transform process, a
comparison between the mean and variance of the data and the transformation is
given and should be approximately the same.
Calculate Estimates:
The program GEODK is used to disjunctive kriging and cokriging. The
disjunctive kriging program allows up to 10 variables to be used for cokriging.
Up to 10 cutoff values can be specified for which the program will calculate the
conditional probability that the estimated value is greater than the cutoff level.
During execution, the output to the screen will use as heading designators the
letters A through J. Typing the F10 key will bring up a window that gives the
definitions of the headings in terms of the cutoff values and transformed cutoff
values .
Line and Block Contour Diagrams:
Line and block contour diagrams are also available from the Disjunctive
Kriging Menu. For more information concerning these programs, see the description
under the Kriging Menu, above.
2.5.k. Modifying and Adding Menus.
It is possible to tailor GEOPACK to an individual's needs by adding programs
or menus to the USER menu (accessed through the F5 key). If the program to be
added to the system requires the use of the data set or any of the output files
produced by GEOPACK, read the help information under the heading SYSTEM OPERATION
on the main HELP menu. The information concerning the files, their contents,
formats, naming conventions, etc. is given by this help sequence.
The following steps are used to add a program or menu to GEOPACK. Several
examples are included in GEOPACK and can be found by typing the *.MEN files. It
is usually easier to start with copy of an existing *.MEN file (or portion
thereof) as a template and make the required modification(s) to the template. To
add a single executable program is very easy, since only a few lines must be added
to an existing *.MEN file. To add an additional menu requires creation of a
complete *.MEN file, and therefore is somewhat more difficult. If a new menu is
to be created, it is generally a good idea to place the *.MEN and executable files
is a new subdirectory.
36
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STEP 1: Determining Whether a Menu or a Program Will be Added:
The first step is to determine whether a menu or a program is to be added
to GEOPACK. If it appears that the application to be added may require several
programs or batch files, it is better to create a new menu containing these items.
An example of creating a menu is the GEOEAS.MEN file contained in the subdirectory
%GEODIR%\USER\GEOEAS, where %GEODIR% is used by GEOPACK to designate the root
directory of the geostatistical programs. The reason for creating a menu rather
than specifying a program is that to run the program GEOEAS requires rewriting the
GEOPACK data file in a format that can be read by GEOEAS. This requires an
interfacing program to create a new file in the proper format.
Next on this menu are the commands for starting the GEOEAS programs. This
is followed by a program which takes the output of the kriging program (in GEOEAS)
and rewrites the output in a format that GEOPACK can read. This enables the user
to utilize the GEOPACK routines on the GEOEAS output. Since each of these
commands concerns the use of GEOEAS it is better to put them into a menu
specifically to run the GEOEAS program, rather than including all these commands
on the USER menu, since space is limited to 11 entries on any one menu.
Step 2: Altering the USER.MEN:
The second step is to alter USER.MEN to include another or alter an existing
heading. Once the program or menu to be added to GEOPACK has been created it can
be accessed through the USER menu (i.e., F5 key) by adding or modifying an entry
to the menu file. Entries to the USER menu are added by editing the USER.MEN
file located in the root of the geostatistical programs (i.e., %GEODIR%\USER.MEN).
An example of a menu entry is:
Line
1: %lE@User Menu
2: *_GEO-EAS
3: #message
4:
5: A%GEODIR%\user.men
6: +%COMSPEC% /c cd %GEODIR%\user\geoeas
7:
8: A%GEODIR%\user\geoeas\GEOEAS.MEN
where the symbols have the following meaning:
I in column 1 indicates that the next two hexadecimal numbers
indicate the Menu colors, where the first and second numbers
are the background and foreground colors, respectively,
and the colors are given by the color-numbers given below
(for example a dark blue background with light yellow
lettering is specified by using "%1E" in line 1, above)
0 - Black 8 - Grey
1 - Blue 9 - Light Blue
2 - Green A - Light Green
37
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3 - Cyan B - Light Cyan
4 - Red c - Light Red
5 - Magenta D - Light Magenta
6 - Brown E - Light Yellow
7 - White F - Light White
In any other column the "%" is used for different purposes.
@ print the following text as the menu title
* print the following text as menu selection heading
# print following text in the information box at the top of
the menu
~ tells the menu program to hold the menu on the screen as
long as possible before switching screens. This helps to
improve the visual appeal of the menu program but should
only be used when "popping" (i.e. , adding) or "pushing"
(i.e., deleting) a menu and not when running an executable
program. It should be placed prior to the menu to be added
or deleted.
+ indicates that the remainder of the line is to be executed.
THE MENU PROGRAM WILL ONLY RUN EXECUTABLE FILES AND NOT
BATCH FILES OR BATCH COMMANDS. To run a BATCH
command the following method must be used:
+ %COMSPEC% /c els - this will clear the screen
+%COMSPEC% /c echo ... - this will echo . . .
+ %COMSPEC% /c cd c:\ - this will call the directory c:\
The name of the file to be executed must be either in the
current directory, include a full path specification or
the file must be in a directory on the DOS path. It is
generally a good idea to include the full path of
every program whether you expect the program to be in the
current directory or not, since it may not be obvious what
the current directory is. You can always change the current
directory using "%COMSPEC% /c CD\
-------
from the right hand side of the screen to the left hand
side; which is done to improve visual appeal). (Push the
menu off the screen).
the underscore before the "G" on line 2 is used to designate
the highlighted character. This character will activate
the menu option. If there are two (or more) menu options
with the same highlighted character, the cursor bar will
move to the next one, each time the highlighted character is
entered.
STEP 3: If Another MENU Is Being Added:
It is often best to place the new program into a separate subdirectory. An
example of this is the GEO-EAS subdirectory which stores the executable programs
for the GEO-EAS geostatistical software system. Once the subdirectory is named
and created, the newly developed program (s) and auxiliary files should be copied
into it. A new data file containing the entries for the newly created menu must
be created using the methods described above. It is probably best to start with
an existing menu command file (e.g. , USER. MEN, GEOEAS.MEN or equivalent) to act
as a template, changing only those lines that are needed. This will provide a
guide for setting up the command file.
In the USER. MEN file, the call to the new menu is made as follows (assuming
that a new subdirectory called "NEWDIR" has been created with the following path:
%GEODIR%\USER\NEWDIR and that the command file for the new menu is called
"NEWMEN.MEN") :
#place a descriptive message for the menu here
*_NEWMEN Menu
A%GEODIR%\user.men
+%COMSPEC% /c cd %GEODIR%\user\newdir
A%GEODIR%\user\newdir\NEWMEN.MEN
The commands necessary to run one (or more) programs from the new menu are
as follows (it is assumed that the new program is called NEWPRG) :
#Quit Menu
*_Quit
*Run _NEWPRG
#place a descriptive message for what the program does here
+%GEODIR%\user\newdir\NEWPRG
The above instructions should be adequate for modifying GEOPACK to include the
new menu and program (s) .
39
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2.5.1. Trouble Shooting.
If an error should occur while attempting to add a program or menu to
GEOPACK try one of the remedies listed below.
1. The newly created USER menu entry does not show up on the USER menu. This
might occur if the wrong menu data file was altered. The proper file to alter
is %GEODIR%USER.MEN. Also , only 11 entries can be placed on one menu. If you
wish to have more than 11 entries you will have to create an additional menu or
move some of the programs to other menus, if they exist.
2. The newly created menu does not run when selected from the USER menu. This is
probably due to an improper path-file name combination. Make sure that the path
and file names are correct. If an error message is printed out by the program,
it is often "lost" because the menu reappears on the screen too quickly. The
error message (or other information) can be seen by typing the F4 key.
3. The newly created menu does not have any entries on it and an error message:
Abort Menu: Menu Data Not Found is printed to the screen. This is caused because
the menu program cannot find the newly created menu data file. This may be due
to changing directories before the new menu is placed on the screen. You should
check to make sure that the commands in the User Menu and the new menu are
appropriate for what you are trying to do.
4. To get back to the USER MENU (located at the right-hand side of the screen,
you have to type two "quits". This is caused because you have popped an
additional USER.MEN on to the screen and the newly created menu only deletes one
of the USER.MEN when you quit the menu. To delete two USER.MEN place two V in
the newly create menu file each on a separate line.
2.6. GEOPACK Enhancements
2.6.a. Running GEO-EAS Geostatistical Software.
The GEO-EAS geostatistical software can be executed from within GEOPACK.
The GEO-EAS programs are accessed by typing the F5 key and selecting the GEO-EAS
option. Since the data set required by GEO-EAS is formatted differently than
GEOPACK, there is an interface supplied to create a data set in. GEO-EAS format.
This data set will have the file extension ".EPA". There is also an interface
program to take the output from the GEOEAS kriging program and convert it to
GEOPACK format. This enables results to be printed and plotted using GEOPACK
graphics capabilities.
2.6.b. Description of GEOPACK Utility Programs.
GEOPACK contains a number of utility programs which can be used separately
from the system to aid in alteration of the system or for use in a "command-line"
mode (i.e., running the program without using the menu system) . A brief
description of the function of each program and their use follows.
40
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Program Name
Description
HELP.EXE This program is used to call a particular help information
section from a file. For example, if you want to print the
help information concerning "Theory of Variograms" the HELP
program could be used as follows: C:\HELP VARI.HLP
THEORY.HLP where VARI.HLP is the help information desired
and THEORY.HLP is the file containing VARI.HLP.
GEOPACK.EXE This program displays the first screen giving the GEOPACK name.
This program also determines where the call to GEOPACK is
made (i.e., the subdirectory where GEOPACK is typed) so that after
leaving the program you will be returned to that directory.
MSDOS.EXE This program allows you to execute a DOS command while run-
ning GEOPACK.
DOSSHELL.EXE This program allows you to leave GEOPACK in a DOS shell and
temporarily suspend execution of GEOPACK. When finished ex-
ecuting DOS commands you reenter GEOPACK by typing EXIT.
MENU2.EXE This is the menu program.
EVOKE.EXE This program is used to execute a program when it is desired
that system parameters be passed to the program. (Note:
system parameters are set by the user and are difficult to
"hard" program). This program is particularly useful when
altering (i.e. , adding additional programs) GEOPACK since it
enables you to pass system parameters to other programs
without having to know their value. For example, to run a
"C " program and passing the location of the temporary
directory, the border color and the text color use:
EVOKE $(TEMPDIR) $ (BORD) $ (TEXT)
EVOKE.EXE substitutes the "true" values for $(TEMPDIR),
$(BORD) and $(TEXT) in the spawning process, i.e., the above
command is equivalent to g:\ 1 11 provided that
the system is setup so that the temporary directory is g:\,
and the border and text colors are 1 and 11, respectively.
The list of parameters EVOKE.EXE can pass follows:
EDITOR - Default text editor
TEMPDIR - Temporary directory
PRINTER Printer device
PLOTTER Plotter device
ROWS - Maximum number of rows on screen
COLS - Maximum number of rows on printed page
TEXT - Text color
BORD - Border color
MODE - Screen mode (0=mono, l=color) This only works in
FORTRAN programs
41
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DSTAT - Default statistics package
LGRAPH - Default line graph package
GRAPH - Default contour, 3-D graphics pkg
DBASE - Default data base management system
Examples: Try these examples in the root of the geos-
tatistical programs
EVOKE defgraf $ (LGRAPH) $ (TEMPDIR) $ (BORD) $ (TEXT)
EVOKE defgraf $(GRAPH) $ (TEMPDIR) $ (BORD) $ (TEXT)
EVOKE $(DBASE) EVOKE DOSSHELL $(BORD) $(TEXT)
EVOKE SDATA $ (TEMPDIR) $ (BORD) $ (TEXT)
EVOKE $(EDITOR)
EVOKE edit $(EDITOR) $(BORD) $(TEXT)
SDATA.EXE This program allows you to declare a data file active by
copying it to the temporary directory (e.g. , RAM drive) and
creating the DEFAULT file which contains the data file name
and origination path. To use type: SDATA from root of the
geostatistical programs.
PACK.EXE This program allows you to take the files on the temporary
subdirectory (e.g. , RAM drive) and store them in an archive
file. These files may be retrieved at a later time using
one Of the programs: EXTRACT.EXE, SDATA.EXE or UNPACK.EXE.
To use type: PACK from root of the geostatistical programs.
UNPACK.EXE This program allows you to take an archived file and remove
all the stored files back to the temporary storage drive
(i.e., RAM disk).
To use type: UNPACK from root of the geostatistical
programs.
EXTRACT.EXE This program allows you to take one or more stored files out
of an archived file and place them on the temporary storage
drive (i.e., RAM drive). You must extract the data file
and the DEFAULT file before attempting to run GEOPACK.
To use type: EXTRACT from root of the geostatistical
programs.
EDIT.EXE This program along with EVOKE allows you to call up the
default text editor for editing the data base. See examples
for using EVOKE for use instructions.
LISTDIR.EXE This program allows you to list the contents of any direc-
tory on a floppy or hard drive. The program also allows you
to view a file.
To use type: C:\LISTDIR
-------
colors-. where the colors are given by the color-numbers
given below:
- Black
- Blue
- Green
- Cyan
- Red
- Magenta
- Brown
- White
8 - Grey
9 - Light Blue
10 - Light Green
11 - Light Cyan
12 - Light Red
13 - Light Magenta
14 - Light Yellow
15 - Light White
VIEW.EXE This program allows you to view the contents of a file. To
use this program type the following: C:\VIEW -
+ file name> where the border and text colors
are given in above. Colors are either decimal as described
above or hexadecimal using a format such as: OxlE.
VED.EXE This program allows you to manually edit the semi-variogram
coefficient file (see the variogram menu and associated
help screens for more information) if it exists.
AUTO.EXE This program operates with the menu system and executes the
necessary commands to create the hard-coded and user-
definable menus.
MGEOEAS.EXE This is an example of a user-written interface to couple the
GEO-EAS geostatistical software to the GEOPACK system. This
program modifies that GEOPACK data file so the GEO-EAS can
read its contents.
MGEOCNVT.EXE This is an example of a user-written interface to couple the
GEO-EAS geostatistical software to the GEOPACK system. This
program modifies the GEO-EAS output file so that GEOPACK can
use the results for further analysis.
SHOWDIR.EXE This program allows you to see a diagram of all the sub-
directories that branch off the current (or specified)
subdirectory. To use type: SHOWDIR .
DEFLT.EXE This program allows you to alter the system settings for the
parameters listed under EVOKE.
To use this program type: DEFLT SYSETUP SYSDEFLT.
43
-------
SECTION 3
EXAMPLES
3.1 VIRUS DECAY RATES IN TUCSON GROUND WATER
Description of Data
Water samples were obtained from 71 continuously pumping public water supply
wells in the Tucson Basin. The water samples were taken to the laboratory and
viruses were added. The samples were incubated at the in situ ground-water
temperature. At predetermined times, subsamples were withdrawn and assayed to
determine the number of virus particles remaining in the water. The decay rate
was calculated as the slope of the line drawn through the data using linear
regression and has the units of Iog10 (virus particles)/day.
Geostatistical Calculations
The data set was configured in the following way according to GEOPACK
requirements and is included in the directory %GEODIR%\USER\DATA under the name,
VIRUS.DAT.
Ground Water Data for the Tucson Basin
2 71
1 2
TEMP
500.00
3 4
DECAY
5
(f5.0,4F10.3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
8.
14.
14.
5.
5
6.
7.
5.
17.
2.
-0
5.
6.
3.
14.
11.
14.
14.
-4.
-5
-1.
5.
9.
.498
.129
.330
.280
.079
.084
.291
.883
.951
.263
.151
.280
.285
.671
.934
.716
.129
.934
.374
.983
.961
.280
.906
7
6
8
8
8
7.
6
5
6
8
9
7
6
7
5
6
4.
4.
11.
12.
10.
6.
4.
.458
.453
.263
.665
.464
.056'
.855
.045
.654
.866
.671
.458
.654
.660
.447
.654
.240
.442
.682
.889
.475
.252
.643
20.
20.
20.
20.
20
23
23
23
23
24
24
24.
24.
24
24.
24.
24
24.
24.
24.
26.
26.
26.
.00000
.00000
.00000
.00000
.00000
.00000
.00000
.00000
.00000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.00000
.00000
.00000
-o.
-0.
-0.
-1.
_ ]_
-0.
-0.
-0
-0.
-0.
-0
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0
-0
-0
-0.
-0
.82800
,94600
.92400
.16400
.06700
.79700
.98900
.89200
.88900
.69500
.85500
.73400
.76900
.80200
.69600
.67600
.96300
.81000
.80500
.81400
.79600
.69900
.76000
44
-------
Step 1: Select a Data Set
To use GEOPACK a data set must be available. Therefore the first step in
using this program is to create a data set (which is assumed to have been done)
and then start GEOPACK and select it.
1) Select Data Set Utilities Menu at Main Menu.
2) Select Select a Data Set at Data Set Utilities Menu.
3) To select the data set, either use the cursor keys to find the entry
VIRUS.DAT or type the name of the file on the keyboard. If a number of files
exist in this directory, it is possible to move the cursor to the first (or next)
file beginning with a specific letter by typing ALT-letter (i.e., hold the ALT key
and type the desired letter). Note: the Select Data program automatically looks
in the "data" directory. This directory is specified in the SYSDEFLT file which
can be altered using the Change System Default Settings program (i.e. , type F3
then C, its the second line on the screen that follows). Once the file VIRUS.DAT
has been selected, GEOPACK reads in the data file, and outputs to the screen the
cutoff level and the number of available data points for the variables. You are
returned to the Main Menu.
Step 2: Check Distribution of Data
The next step in the analysis is to determine if the data are normally
distributed. Although the kriging technique does not required the data to have
a normal distribution (and is a best linear unbiased estimator regardless of the
distribution of the data) the estimator is optimal whenever the data is normally
distributed.
4) Select Statistics Menu.
5) Select Kolomogorov Test of Distribution.
6) Select the appropriate data set, in this case, B, decay. The calculations
are output to the screen. At this time, you may type J to jump ahead. The
results of the Kolomogorov-Smirnov Test for Distribution are output to the screen.
In this case, we accept the null hypothesis at the 0.05 level and thus there is
some evidence that the data are normally distributed. If the data were not
normally distributed, it would be possible to transform the data into a new data
set with a normal distribution. A logarithmic transformation is a common
technique for transforming data into a normal distribution. You are returned to
the Statistics Menu.
Step 3: Determining the Variogram
Next the sample spatial correlation structure (i.e., the sample semi-
variogram) must be determined. Without this functional relationship between the
distance and the variance it is not possible to use the kriging techniques.
7) Select Variogram Menu.
8) Select Variogram Calculation (Sample).
9) Select type of correlation function, in this case, A, semivariogram.
46
-------
10) Select the principal function, in this case, B, decay.
11) You will now be asked several questions about how you want the calculations
performed, unless you have set up the default settings file in such a manner as
to avoid this. When responding to the questions, you may either type in a number
or push Enter to select the default value which is shown on the lower left-hand
side of the screen.
12) After all of these questions have been answered, the variogram is calculated.
The progress of the calculations is output to the screen as Percent Completion on
the lower right-hand side.
13) Both a table of values and a plot of the sample variogram are printed to the
screen. For this data set, the output appears as shown in Figure 3.1.1 (Note: the
following figures use the device drivers supplied with GEOPACK. Publication
quality figures can be created using an appropriate graphics package and the USERS
MENU (F5).
14) You are now given several options. Select Options to add labels to your
graph. Upon Exiting this menu, you are returned to the Variogram Menu.
15) Select Automatic Model Fit.
16) You will again be asked several questions, then allowed to choose the
autocorrelation function you wish to model.
17) Select a model type, in this case, D, spherical. The input parameters are
printed to the screen, as well as the input data. If you wish to delete any of
the data, type D, Enter, the Observation number, and Enter. You need to repeat
this step for each line you want to delete. In this case, we delete lines 8
through 12.
18) Several screens will be printed, detailing the results of the model variogram
calculations . The model fit to the data will then be printed to the screen. For
this example, the output is as shown in Figure 3.1.2.
19) Once again, you are given the opportunity to add labels, etc. to the graph,
20) Upon Exiting the screen, you are asked if you want to rerun the program. If
No, you are returned to the Variogram Menu.
21) Select Manual Model Fit, Select Model(s).
22) You now select the desired file by hitting Enter.
23) A summary of the models that you have run on that data file is then shown.
Type S to save the correlation model that you want to krig.
24) You are returned to the Variogram Menu.
Step 4: Create a Grid of Estimates Using Ordinary Kriging
The final step in this example is to obtain a grid of estimates using the
data set and the model of the spatial correlation structure. An estimate can be
made at any point in the field of interest. In general, estimates made far from
any data points will have a higher estimation variance (i.e. , there is less
confidence that the estimate is close to the true value) compared to estimates
made close to data points. If an estimate is made at the same coordinates as one
of the data points in the data set, the estimated value will exactly equal the
data value at that point and the estimation variance will be zero. This behavior
indicates that kriging is an exact interpolator.
25) Select Ordinary Kriging. You will be asked several questions unless you
have modified the Default Settings file to avoid this.
47
-------
26) Several screens showing the output from the kriging calculations will be
output to the screen. Once again, at the Kriging Estimates for Decay screen, you
are given the opportunity to Jump ahead and bypass seeing the output of this
program.
27) When the program is finished, you are returned to the Ordinary Kriging Menu,
where you select Line Contour Plot.
28) You are given the choice of plotting the estimated value or the variance.
In this case, we choose A, and the following contour plot is shown on the screen:
29) You are given the option to add labels to the plot as before.
30) After Exiting this program, you are returned to the Ordinary Kriging Menu.
31) This time, we select Block Contour Plot.
32) Again we choose A to plot the estimated values, and the output looks like the
following:
48
-------
e = .0-
DATE: 09/01/1989
SEMIVARIOGRAM
No. OF
LAG COUPLES
1
2
3
4
5
6
7
8
9
10
11
12
11
125
232
230
249
241
216
193
160
175
137
146
DISTANCE
.41
1.23
2.38
3.54
4.65
5.83
6.95
8.17
9.38
10.50
11.66
12.77
CALCULATION 56 » ± 90.0'
TIME: 09:06 am
SEMIVARIOGRAM DRIFT
DECAY DECAY
.0243 -.1444
.0292 -.0649
.0366 -.1125
.0415 -.1355
.0426 -.1603
.0437 -.1633
.0424 -.1621
.0379 -.1557
.0342 -.1586
. 0406 - .1680
.0574 - .2497
.0426 -.1555
A
Strike a key when ready . .
X R|0|H|
Virus Data
8,845
8,83
8.825
B
Distance (km)
Figure 3.1.1. Example output from Variogram Calculation (Sample) program for the
data set, VIRUS.DAT. in A and B, respectively, are the tabular values and a plot
of the semivariogram function.
49
-------
8,85
8,845
0,84
8,035
18,8
8,825
0,82
8,815
8,01
Virus Data
Distance (km)
18
Figure 3.1.2. Example output from the Automatic Model Fit program. The solid
line is an spherical model that was fitted to the sample semivariogram.
50
-------
SUMMARY OF SPATIAL CORRELATION
Line No. Sill -
No. Pts DIR MODEL NUGGET NUGGET
1 10 .00 EXPON .0165 .0240
[ 2.33] [ 3.55]
2 10 .00 SPHER .0207 .0197
[ 5.34] [ 4.98]
3 10 .00 POWER .0000 0311
[ .00] [ .16]
Esc: Exit Fl : Help S: Save V: View
MODELS
RANGE
1.2286
[ 2.00]
3.8252
[ 3.52]
.1297
[ .19]
M: Model
SSQ
.00008
.00007
.00016
(Manual Mode)
A
= Variables
TEMP / TEMP
TEMP / DECAY
DECAY / TEMP
DECAY / DECAY
Variogram Editor: File: G:\VIRUS.VAR
Model ' Nugget == Si 11-Nugget = Range =
None 0 0 0
None 0 0 0
None 0 0 0
Spherical 0.021 0.02 3.825
00
B
ESC: Exit
Fl: Help
F2 : Save
Home
End | _ Page Up | | Page Do;
Figure 3.1.3. Example output from Manual Model Fit,
A) and the Edit Variogram Model File (in B) .
Select Model (s) program (in
51
-------
Virus Decay Kate
Distance (km)
Figure 3.1.4. Contour diagram of the estimated value of the decay rate using the
Ordinary [Co]Kriging and Line Contour Diagram programs is illustrated.
52
-------
HI•<•)«>
-------
3.2. SALINITY IN A SOUTHWEST ARIZONA FIELD.
Description of Data
This data set contains two random functions, the electrical conductivity
(EC), and the sodium adsorption ratio (SAR). The data was collected by Al-
Sanabani (1982) at 101 random locations on a 1m by 1m grid system in a 10-ha
field (soil type: Typic Haplargid). The 1-2 kg samples were placed in a beaker
with distilled water and a saturated paste was made. The solution was extracted
from the paste and the EC of the solution measured. A more detailed description
of the data and techniques used to measure the EC and SAR is given in Al-Sanabani
(1982) . This data set is included" in the %GEODIR%\USER\DATA directory under the
name, ECSAR.DAT.
Step 1: Check Distribution of Data
The hypothesis that the data were normally or lognormally distributed
was tested using the Kolomogorov-Smirnov (KS) test for goodness-of-fit (Sokal
and Rohlf, 1981; Rao et al., 1979). The KS test statistic was calculated
and compared to the critical value at the 0.1 probability level. This level
was chosen to reduce the probability of the type II error, namely the probability
of incorrectly selecting the null hypothesis (Rao et al. , 1979).
For a sample size greater than 30 the critical value at the a= 0.1
probability level can be obtained from the asymptotic expansion (Rohlf and
Sokal, 1981; Rao et al., 1979):
K Scrit = 0.805/(7n)
The results of the KS test indicate that the original and log-
transformed data are from lognormal and normal distributions respectively,
at the 0.1 probability level. Therefore a lognormal transformation will cause a
data set to have a normal distribution. The KS test statistic calculated from the
data sets were 0.197 and 0.065 for the original (EC) and transformed (InEC) data,
respectively. The associated critical value is 0.080 and was calculated by Eq.
1 for n = 101. Since the data are lognormally distributed, they will be
transformed to a data set with a normal distribution by taking the logarithm of
each datum. This new data set will be used for the geostatistical analyses.
Step 2: Transform the Data Set
The data set can be transformed by using the Modify an Existing Data Set
option on the Data Set Utilities Menu. The steps necessary to use this program
to add a random function called In [EC] by taking the logarithm of the EC data are:
1. The allowable transformations can be viewed by typing Fl (Help) before
selecting the variable to modify. Place the lightbar over the data set (i.e., EC)
to be transformed. Type Enter.
2. Move the lightbar over one of the Unused markings and type Enter. A window
will pop up in which the name for the new data set can be entered. In this case,
the new data set will be called In[EC].
54
-------
3. Type in the transform equation, which for this example is:
y=log(x); (natural logarithm)
and type a F4 to start the transformation process. Once completed both the EC and
In [EC] data sets will exist in the data file.
4. To save the transformation results, type F2 and either 0 to overwrite the data
file or B to save a backup copy of the old data file. If you decide you do not
want to save the new data set, the type ESCAPE and you will be asked if you want
to leave the program without making any changes.
5. To exit, type ESCAPE.
Step 3: Determining the Variogram
As with all kriging methods some measure of the spatial correlation
structure is necessary. For disjunctive kriging the appropriate function is the
auto correlation which requires a second-order stationary hypothesis (i.e. , the
variance must be finite).
An easy method for determining the autocorrelation from the semi-variogram
is to use the following relationship
p(h) = 1 -r(h)A<«)
which is done automatically when using the disjunctive kriging program. Using
GEOPACK to determine the sample semivariogram by following the sequence given in
Example 1. Next a model variogram is applied to the sample semivariogram. For
this example, the automatic fitting procedure is used and yields
•y(h) = 0.27 + 0.66 [1.5h/145 - 0.5 (h/145)3] ; 0 145
and is shown in Figure 3.2.1.
This variogram model was used in the cross validation procedure listed on
the Ordinary [Co]Kriging Menu which attempts to fit both the sample semi-variogram
and the reduced mean and variance simultaneously. An acceptable model variogram
is given when the reduced mean and variance are approximately 0.0 and 1.0,
respectively, subject to a reasonable fit to the original sample semivariogram.
Using the Cross Validation procedure on the Ordinary [Co]Kriging Menu, the reduced
mean and variance of the above model can be determined and are, respectively,
.0198 and 1.224.
The cross-validated model is somewhat different from the one listed above
because now the fitting procedure also tries to fit the reduced mean and variance.
For this case the semi-variogram model is
f(h) = 0.36 + 0.52 [1.5h/153 - 0.5 (h/153)3] ; 0 153
55
-------
For the model given above, the reduced mean and variance, respectively, were
0.0241 and 1.062. One problem in using the reduced mean and variance for
determining the adequacy of semivariograms is that there is no independent method
for determining how close to zero and unity the reduced mean and variance should
be and therefore using this technique to fit models to a variogram is somewhat
subjective.
Viewing the two variograms using the Fit Models Manually option on the
Variogram Menu, it appears that the neither of the models produces an adequate fit
for both the sample semivariogram and reduced mean and variance. For this reason,
an alternative model is chosen that falls in between the cases listed above. This
model is
•y(h) = 0.30 + 0.60 [1.5h/160 - 0.5(h/160)3] ; 0 < h < 1 6 0 [5]
•y(h) = 0.90 = ?(«); h > 160
and has a reduced mean and variance, respectively, of 0.0203 and 1.19.
Step 4: Calculate the Hermite Coefficients
The next step in the disjunctive kriging process is to find the coefficients
which define the Hermite transform function (See Theory of Geostatistics listing
on the GEOPACK User's Manual, Type Fl) . To obtain the Hermite coefficients it
is necessary to select the Hermite Coefficients listing on the Disjunctive Kriging
Menu. There are a number of questions that must be answered during the execution
of this program. These questions will appear only if the Set Program Parameter
program was not run prior to this selection.
Step 5: Create a Grid of Estimates Using Disjunctive Kriging
A total of 2500 estimates of EC and In(EC) (using each method) were obtained
on a 5 by 5 meter grid system superimposed over the field sampled by Al-Sanabani
(1982). Along with each estimate a value of the kriging variance was calculated
and for the disjunctive kriging method a value of the conditional probability.
Bower and Wilcox (1965) gives 4.0 dS/m as a critical value of EC for many plants
therefore this value (or the In(4.0 dS/m) ) was used for the critical value (i.e. ,
Zcut) in subsequent analyses. For all cases a maximum of 5 nearest neighbors
within a radius equal to the range of the variogram were used in the estimation
process. Next, the results were contoured to show the spatial distribution of
the electrical conductivity and illustrated in Figure 3.2.2.
Step 6: Create a Grid of Conditional Probability Estimates
The disjunctive kriging estimator can also be used to determine the
conditional probability that the unknown value is greater than a specified cutoff
value. An example of this is given in Fig. 3.2.3 where the conditional
probability that the ln[EC] is greater than ln(4.0), respectively is contoured.
56
-------
From this figure one can see that the zones of high probability coincide with
areas of high In [EC] . Although the shapes of the high probability zones are
similar to the shapes of the In [EC] contours in Fig. 3.2.2, two points with the
same estimated value of In [EC] do not always produce the same conditional
probability. For more information see Yates et. al. (1986)
Salinity
Distance (n)
Figure 3.2.1. The semivariogram function for the natural logarithm of the
electrical conductivity using the Variogram Calculation (Sample) program and the
data set, ECSAR.DAT.
57
-------
level 1
Level 2
Level 3
' eve! 4
?vel 5
evel 6
evel 7
evel 8
-8.1894 <= jiiiiilJIK 8.6179
8.6179 <= < 8.826
8.826 <=
1.049 <=
1.229 <=
1.347 <=
1.491 <=
1.752 <=
1.849
1.752
< 2.636
Figure 3.2.2. Contour diagram of the estimated value of the electrical
conductivity using the Disjunctive [Co]Kriging and Block Contour Diagram programs.
58
-------
Figure 3.2.3. Contour diagram of the conditional probability that the estimated
value of the electrical conductivity is greater than the natural logarithm of 4
dS/m (i.e., 1.38 log(dS/m}) using the Disjunctive [Co]Kriging and Block Contour
Diagram programs. This figure shows the actual screen position of the contour
levels window when displayed.
59
-------
3.3. SURFACE MOISTURE, TEMPERATURE AND SOIL TEXTURE.
Description of Data
This data set contains three random functions, the surface moisture content,
(9) , the surface soil temperature (T) and the sand content of the surface 1 cm.
The moisture content and sand content data were collected at 71 random locations
and the temperature data at 120 random locations on a 1m by 1m grid system in a
1 ha field at the Campbell Agricultural Center of the University of Arizona. A
more detailed description of the data and techniques used to measure the EC and
SAR is given in Yates and Warrick (1988) . This data set is included in the
Available Data Sets option (Type: F5, followed by A) and is named C912.DAT.
Step 1: Determining the Variogram
As with all kriging methods some measure of the spatial correlation
structure is necessary. For cokriging a spatial correlation function is required
for each random function as well a cross-correlation function for each pair of
random functions to be included in the analysis. Since ordinary kriging is to be
performed it is only necessary that the random functions be intrinsic (i.e., it
is no longer required that the variance be finite) .
GEOPACK is used to determine the sample semivariogram by following the
sequence given in Example 1, Next a model variogram is applied to the sample
semivariogram. For this example, the automatic fitting procedure is used and
yields the following exponential models
•y(h) = 0.00 + 34.2 (1 - exp [-h/8 . 78] ) ; for surface moisture
•y(h) = 0.00 - 18.4 (1 - exp [-h/10 .8] ) ; for cross-semivariogram
•y(h) = 2.86 + 15.6 (1 - exp [-h/4 . 71] ) ; for surface temperature
for h > 0 and are shown in Figures 3.3.1 and 3.3.2. The overall reduced mean and
variance for this set of variograms is -0.0091 and 0.92, respectively.
This variogram model was used in the cross validation procedure listed on
the Ordinary [Co] Kriging Menu which attempts to fit both the sample semi -variogram
and the reduced mean and variance simultaneously. Since only one model can be
cross-validated at a time the following method was used. First the semivariogram
for the surface moisture was cross-validated. This was followed by cross-
validating the surface temperature model. Assuming that these semi -variograms
were not affected by the cross-validation of the cross-semivariogram, they were
fixed during the cross-validation of the cross-semivariogram. Using this Cross
Validation procedure the following variogram models
= 0.00 + 34.0 (1 - exp [-h/8. 23] ); for surface moisture
Y(h) = 0.00 - 18.3 (1 - exp [-h/10 .3] ); for cross-semivariogram
y(h) = 4.19 + 14.3 (1 - exp [-h/5 . 12] ) ; for surface temperature
60
-------
for h > 0 were calculated. The overall reduced mean and variance for this set of
variograms is -0.0068 and 0.88, respectively. Plots of the model variograms and
the sample variograms are shown in the Figures. Viewing the cross-validated
variogram models using the Save Model(s). Fit Models Manually option on the
Variogram Menu indicates that either set of variogram models would be adequate
representations of the spatial correlation structure.
Step 2: Create a Grid of Estimates Using CoKriging
A total of 2500 estimates of the surface moisture content were obtained on
a 2 by 2 meter grid system superimposed over the CAC field site using cokriging.
(the auxiliary variable was the surface temperature). Along with each estimate
a value of the kriging variance was calculated. Shown in Fig. 3.3.3 is a block
contour diagram of the cokriging estimates and definition of the color/pattern
used in the diagram. For this example a maximum of 5 nearest neighbors of the
moisture and temperature within a radius of 20 m from the estimation site was
used in the estimation process. Shown in Figure 3.3.4 is the associated
estimation variance for the soil moisture using the cokriging technique.
61
-------
32
28
£ 21
g1
1 28
* 16
12
22
en IA
.2 12
is
1 18
Soil tloisture
12
12
Soil Itnperature
Distance (n)
0 0 1
-0 2
B
Figure 3.3.1. The semivariogram function for the surface moisture content (in A)
and the surface soil temperature (in B) using the Variogram Calculation (Sample)
program and the data see, C912.DAT.
62
-------
Soil Boisture and lenperature
Distance (n)
Figure 3.3.2. The cross-semivariogram function for the surface moisture content
and the surface soil temperature using the Variogram Calculation (Sample) program
and the data set, C912.DAT.
63
-------
Level 1
Level 2
Level 3
Level 4
Level 5
Level 6
Level 7
Level 8
1.4471
5.9127 <
7.1459 <
8.1546 <
9.3162 <
18.872 <
13.079 <
16.831
<=
<=
< 5.912?
< 7.1459
< 8.1546
< 9.3162
< 18.872
< 13.079
< 16.831
< 24.674
Figure 3.3.3. Contour diagram of the estimated value of the electrical
conductivity using the Ordinary [Co]Kriging and Block Contour Diagram programs.
64
-------
REFERENCES AND SUGGESTED READING
Abramowitz, M. and A. Stegun, Handbook of Mathematical Functions, Dover
Publications, Inc., New York, 1965.
Al-Sanabani, M., Spatial Variability of Salinity and Sodium Adsorption
Ratio in a Typic Haplargid Soil, M.S. Thesis, The Univ. of
Arizona, Tucson, 1982.
Baafi, E.R., Program User's Manual for Basic Geostatistics System, Unpublished
Report, Dept. of Mining and Gee. Eng., Univ. of Arizona, 50 pp. , 1982.
Bell, K.R, B.J. Blanchard, T.J.Schmugge and M.W. Witczak, Analysis of
Surface Moisture Variations Within Large-Field Sites, Water
Resour. Res. 16:796-810, 1980.
Bhattacharyya, G.K. and R.A. Johnson, Statistical Concepts and Methods,
John Wiley, New York, 639 pp., 1977.
Bower, C.A. and L.V. Wilcox, Soluble Salts, In: Methods of Soil Analysis
Part 2, C.A. Black, Ed., Monograph No. 9, Am. Soc. Agronomy,
Madison, WI, pp. 933-951, 1965.
Burgess, T.M. and R. Webster, Optimal Interpolation and Isarithmic Map-
ping of Soil Properties. I. The Semivariogram and Punctual
Kriging, J. Soil Sci. 31:315-331, 1980a.
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