Geostatistical Software for Conducting Analysis of the Spatial Variability of One or More Random Functions


GEOPACK is a comprehensive EPA geostatistical software system for conducting analysis of the spatial variability of one or more random functions. GEOPACK is menu-driven, user-friendly, and includes on-line help. Basic statistics including mean, median, variance, standard deviation, skew, kurtosis and max/min values can be determined. Includes linear and polynomial regression, Kolomogorov-Smirnov test for distribution and calculation of several percentiles of a data set. The sample semivariogram, cross-semivariogram or semivariogram for combined random functions for a two-dimensional spatially-dependent random function can be determined. Ordinary kriging and co-kriging estimators in two dimensions along with their associated estimation variance and the conditional probability that the value is greater than a specified cutoff level. Graphics capability, including linear or logarithmic line plots, contour plots and block (pixel) diagrams, is included. Device drivers for HP plotters, LaserJet and dot matrix printers are included. GEOPACK includes the source, executable code, documentation, and technical support.


The GEOPACK 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 simple to use, requiring a minimum number of input data.
GEOPACK uses dynamic allocation of memory so that data sets with a wide range of variables and positions can be used without having to alter the program. A large storage array is partitioned based on the number of samples and variables so that there is little wasted space compared to defining the arrays to have a fixed number of samples and variable. One limitation is that GEOPACK allows a database (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 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 menu 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 for generating statistics, line graphics, surface graphics, text editing and database management systems. The program names are defined in the GEOPACK System Default Settings file. Other miscellaneous user-defined programs can also be incorporated into GEOPACK.

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 database (i.e., a file containing one or more random functions plus their x and y coordinates). Programs are also included for:


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.
A model can be fitted to the sample semivariogram using the nonlinear least- squares fitting procedure. This provides a first estimate for the coefficients to be used in a cross-validation program and helps to automate the model-fitting procedure. If the least squares technique fails, or other information is available which should be included in the model-fitting process, the traditional iterative method of 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 co-kriging 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 co-kriging 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 Output

Various graphics capabilities are included such as linear or logarithmic line plots, contour and block (i.e., pixel) diagrams. Device drivers for the HP LaserJet, 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. 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.
GEOPACK data files must be created in the proper format. A text editor may be used to create or modify the data files. For GEOPACK to function properly, the data set must contain at the minimum:

Line Contour Diagram

A contouring package is provided with GEOPACK so that the output files from the kriging program can be graphically illustrated. The contouring program reads an output file and produces a file 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.

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Incredible NetworksΤελευταία Ενημέρωση 27 Ιουλίου 2004 - Last Revised on July 27th, 2004
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