DISJUNCTIVE KRIGING FOR ENVIRONMENTAL MANAGEMENT

Abstract

Land managers, legislators and law enforcement agencies must often make decisions based on critical thresholds and using estimates that are subject to error. Disjunctive kriging enables this error to be converted to an estimated probability that the true value exceeds the threshold, thereby giving the decision-maker a means to judge the risk of taking the estimate at its face value. This paper describes Gaussian disjunctive kriging, the most common form of the technique for continuous variables of the kind generally encountered in environmental management. The variable is assumed to be the outcome of a second-order stationary random process. Its distribution may be of almost any kind, and it is transformed to normal using Hermite polynomials. The Hermite polynomials, which are orthogonal, are kriged independently, and from them are obtained estimates of the original variable, estimates of the kriging variances, and estimates of an indicator, which may be treated as estimates of the conditional probabilities that a threshold is exceeded. The technique is illustrated with two case studies. One analyses total cadmium and easily extractable copper concentrations in the soil of England and Wales from data in the National Soil Inventory. It shows where cadmium (Cd) is likely to be toxic and where copper (Cu) might be expected to be deficient for crop plants and animals. The other examines soil salinity arising from irrigation in the Bet Shean valley of Israel using values of the electrical conductivity of the soil (EC), and a single threshold value. There, although soil in about half of the region has an estimated EC less than the threshold, the probability of exceeding the threshold on the sampling evidence is fairly large almost everywhere.