Mathematical Geology, Vol. 30, No. 1, 1998 Ordinary Cokriging Revisited 1 P. Goovaerts 2 This paper sets up the relations between simple cokriging and ordinary cokriging with one or several unbiasedness constraints. Differences between cokriging variants are related to differences between models adopted for the means of primary and secondary variables. Because it is not necessary for the secondary data weights to sum to zero, ordinary cokriging with a single unbiasedness constraint gives a larger weight to the secondary information while reducing the occurrence of negative weights. Also the weights provided by such cokriging systems written in terms of covariances or correlograms are not related linearly, hence the estimates are different. The prediction performances of cokriging estimators are assessed using an environmental dataset that includes concentrations of five heavy metals at 359 locations. Analysis of reestimation scores at 100 test locations shows that kriging and cokriging perform equally when the primary and secondary variables are sampled at the same locations. When the secondary information is available at the estimated location, one gains little by retaining other distant secondary data in the estimation. KEY WORDS: cokriging, unbiasedness constraints, negative weights, standardization. INTRODUCTION Depending on the model adopted for the random function, three kriging variants can be distinguished: simple kriging, ordinary kriging, and kriging with a trend model (universal kriging). Several authors (Matheron, 1970, p. 129; Journel and Rossi, 1989) showed that the latter two algorithms are but simple kriging with the stationary mean replaced by a local mean that is estimated within each search neighborhood. Similar relations exist in the multivariate situation and are developed here for the most frequently used simple and ordinary cokriging. Moreover, the cokriging system for estimating the local primary and secondary means implicitly used in ordinary cokriging is established. The unbiasedness of the ordinary cokriging estimator is ensured by forcing the primary data weights to sum to one whereas the weights of each secondary variable are constrained to sum to zero. Under these "traditional" constraints 1 Received 9 September 1996; accepted 8 April 1997. 2 The University of Michigan, Department of Civil and Environmental Engineering, EWRE Bldg., Room 117, Ann Arbor, Michigan 48109-2125, U.S.A. e-mail: goovaert@engin.umich.edu 21 0882-8121/98/0100-0021$15.00/1 © 1998 International Association for Mathematical Geology