The state of environment (air, water, etc.) is described by observations and by deterministic simulations based on the physico-chemistry or the biology of complex phenomenons. But the measurements differ from the results of deterministic simulations, mainly because the spatial support of observations is generally ponctual, whereas the values given by the simulations represent rather averaged quantities on the grid.
In order to enhance the estimates and improve their realism, a ?simple? bivariate model between the observations and the deterministic simulation is generally applied. The variable of interest Z is split in two terms ; one is proportional to the deterministic simulation S, and the other is a ?residual? R, supposed to be non correlated (spatially or temporally) with S : Z = a + b S + R The observations O are modeled introducing a measurement error D : O = Z + D
However, the joint exploratory analysis of data and simulation results show that this bivariate model is not always suited. The study of air pollution concentrations or of water « parameters » shows that a linear model of coregionalisation can be much more advisable. The interpretation of the intrinsic correlation model between the variable Z and its deterministic simulation S (Chilès et Séguret, 2008) is generalized to the linear model of coregionalisation. This gives a powerful method to detect the imperfections of the deterministic simulations. The consequences of those relations on the estimation are then examined.