Optimization strategies for spatial sampling of air quality measurement surveys
Résumé
A spatial statistical methodology is proposed to design benzene air concentration measurement surveys at the urban scale. In a first step, an a priori modeling is based on an analysis of data coming from previous campaigns on two different agglomerations. This analysis suggests a modeling that consists of a drift plus a spatially correlated residual. The statistical analysis performed leads us to choose the most relevant auxiliary variables and to determine an a priori variogram model for the residual. Moreover, as the fitted values of the variogram parameters vary from a campaign to another, an a priori distribution is defined to account for those variations. In a second step, we optimize the positioning of the measuring devices on a third agglomeration according to a Bayesian criterion. Practically, we aim at finding the design that minimizes the mean over the urban domain of the universal kriging variance, whose parameters are based on the a priori modeling, while accounting for the prior distribution over the variogram parameters. Heuristic global optimization methods are applied and compared. We also show how this methodology can be useful to determine the number of sensors needed in the survey.