VARIOG2D: a computer program for estimating the semi-variogram and its uncertainty

Abstract

VARIOG2D is a Fortran-77 program that provides four basic operations for semi-variogram analysis: inference of the experimental semi-variogram, estimation of the variance–covariance matrix of the experimental semi-variogram, fitting a theoretical model by non-linear generalised least squares and estimation of the uncertainty of the semi-variogram model parameters. Although software for estimating the semi-variogram by the method of moments is widely available, there is no generally available software for assessing the uncertainty of the experimental semi-variogram. VARIOG2D provides the exact variance–covariance matrix of the experimental semi-variogram, which can be used for attaching standard errors to the experimental semi-variogram, for assessing the correlation between the different semi-variogram lag estimates and for fitting a model by generalised least squares. In addition, the generalised least-squares fitting procedure allows an evaluation of the uncertainty of the experimental semi-variogram and of the semi-variogram model parameters. A case study shows the application of the variance–covariance matrix of the experimental semi-variogram and the performance and capabilities of the program.