Correcting for negative weights in ordinary kriging

Negative weights in ordinary kriging (OK) arise when data close to the location being estimated screen outlying data. Depending on the variogram and the amount of screening, the negative weights can be significant; there is nothing in the OK algorithm that alerts the kriging system about the zero threshold for weights. Negative weights, when interpreted as probabilities for constructing a local conditional distribution, are nonphysical. Also, negative weights when applied to high data values may lead to negative and nonphysical estimates. Ln these situations the negative weights in ordinary kriging must be corrected. An algorithm is presented to reset negative kriging weights, and compensating positive weights to zero. The sum of the remaining nonzero weights is restandardized to 1.0 to ensure unbiasedness. The situations when this correction is appropriate are described and a number of examples are given. Copyright (C) 1996 Elsevier Science Ltd.