Optimal spatial design for air quality measurement surveys: what criteria?

In this work, we present a spatial statistical methodology to design benzene air concentration measurement surveys at the urban scale. In a first step, we define an a priori modeling based on an analysis of data coming from previous campaigns on two different agglomerations. More precisely, we retain a modeling with an external drift which 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. An a priori distribution is also defined for the variogram parameters, whose values appear to vary from a campaign to another. 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. Two optimization algorithms are then compared: simulated annealing and a particle filter based algorithm.