REVISITING THE ACCURATE CALCULATION OF BLOCK-SAMPLE COVARIANCES USING GAUSS QUADRATURE

Block-sample covariances may be calculated by discretizing a block into regularly spaced grid points, computing punctual covariance between each grid point and the sample, then averaging. Gauss quadrature is a better, more accurate method for calculating block-sample covariance as has been demonstrated in the past by other authors (the history of which is reviewed herein). This prior research is expanded upon to provide considerably more detail on Gauss quadrature for approximating the areal or volumetric integral for block-sample covariance. A 4 x 4 Gauss point rule is shown to be optimal for this procedure. Moreover, pseudo-computer algorithms are presented to show how to implement Gauss quadrature in existing computer programs which perform block kriging.