Which relations between deterministic simulations and observations?
Résumé
The state of environment (air, rivers and groundwater, etc.) is described by observations on one hand and by deterministic simulations based on the physics and chemistry and/or on the biology of complex phenomenon on the other hand, with results that usually differ. Generally the deterministic simulation is less variable than observations, but the differences cannot be explained by the only differences of support between observations (spatial "point" values) and simulation results (representing rather averaged quantities on the grid). In order to enhance the simulation to match the observations, a "simple" bivariate model consists in splitting the studied variable Y as the sum of the deterministic simulation S and a correction term R which is supposed to be not correlated (spatially or temporally) with S: Y = S + R. The observations Z differ from Y by a measurement error term. Within this model, the estimation of Y from the observations Z can be reduced to the kriging of the residual R from the " innovations " Z - S at observation points. Joint exploratory analysis of observations and results of deterministic simulations shows that this bivariate model does not always suit to the data. Innovations appear to be correlated with the simulation S. In order to take such correlations into account, Chilès, Séguret et al. (2008) proposed an intrinsic correlation model between the variable Y and the deterministic simulation S. This intrinsic correlation model is generalized here to the linear model of coregionalization. Examples are presented in air and river quality modeling. Consequences for the estimation are examined.