Submitted to: Computers and Geosciences
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/26/2001
Publication Date: N/A
Interpretive Summary: Many fields of pure and applied science use statistical methods to study the variability of a measurement or property in both space and time. Often an estimate of the scale of variability in time or space is the principle interest of an investigation or a necessary step for further analysis. Many of the computational methods used to estimate the scale of variability are based on simple restrictive assumptions that may not always be valid. In this research, we developed an alternative method that is less restrictive and demonstrated its use with a simple example. (Also the computer code for the method is provided in a commonly available computer language.) In many cases, the new method is simpler and easier to apply to a specific problem. Researchers and managers who need estimates of variability scales in time or space can add this method to their computational toolkit.
Technical Abstract: Empirical semivariograms are not always readily modeled with the common simple parameterizations like the spherical model. When averaging lengths are the goal of the variographic investigation, modeling the rising portion is unnecessary. This paper presents an alternative numerical method for estimating the range. Also included is an example using a simulated semivariogram. An initial guess for the sill is required then a numerical integration of the related correlogram is repeated until the sill value converges. The method estimated the range within 0.5% on the given example and within a few percent on several others. Some guidelines for using the algorithm are provided along with a few cautions. Although the program code is written using SAS, the method is general and can be done in many other programming languages. The program code is listed in the appendix.