Collocated Cokriging

Abstract

Consider two coregionalized variables Z(u), the primary variable, and Y(u), the secondary vari‐ able where u refers to locations in a stationary domain. The primary variable Z(u) is sampled at n locations. The secondary variable Y(u) is measured at all locations within the domain. The Y(u) variable is used to inform the prediction of Z(u). Only one secondary variable is considered for this lesson; if multiple secondary variables are present, the simplest solution is to aggregate secondary variables into one super secondary variable (see the lesson on supersecondaries). The complete implementation is demonstrated in an accompanying Python notebook. Cokriging uses the resulting aggregated super secondary variable (Yang&Deutsch (2019)). Tradi‐ tionally cokriging with a linear model of coregionalization (LMC) is used in multivariate estimation; however, due to the complexity of the cokriging workflow, other techniques were developed for scenarios with exhaustively sampled secondary data. Collocated cokriging simplifies estimation by using an intrinsic model and the collocated secondary data. This lesson will explain and compare the different methods of collocated cokriging. To help simplify the lesson it will be assumed that the variables Z(u) and Y(u) have been standardized or normal score transformed and have a mean of zero and a standard deviation of one (see the lesson on the normal score transformation).