Spatial air pollution modeling generating design of measurement network

In this work we are aiming at unification of information about spatial behavior of long-term average concentration of selected air pollutants coming from both measurement and numerical modeling on a large spatial scale. Statistical model that we develop is of inherently Bayesian nature and reflects both detailed spatial features (background and urban increment Markov random fields) and calibration of numerical model outputs (CAMx and Symos model outputs coming as covariates in the comprehensive model). We fit the model in a computationally highly effective way based on INLA (Integrated Nested Laplace Approximation). While such a model is of independent interest for spatial interpolation allowing for both details (such as effects of major highways) and good calibration against empirical data, we will focus on its use for design problems related to the measurement network. Statistical design principle that we develop is derived from the model consequences in a fully formalized, probabilistic way. Namely, our design approach is of mini-max type (minimizing maximum interpolation standard error over a grid covering area of interest with respect to placement of measurement points). Due to the construction of our Bayesian model, the design accounts for both regression (non-empirical, related to numerical modeling) and spatial interpolation (empirical, measurement related spatially autocorrelated field) parts and reflects various types of uncertainties that are typically overlooked. Since we have access to the posterior distribution of the comprehensive statistical model structural parameters, we can reflect uncertainty in their estimates and assess the effects it has upon the selection of measurement design points. Using our stepwise design point selection algorithm, we will illustrate several tasks of different complexity related to the network design: reduction (omitting pre-specified number of stations), improvement (moving existing stations to improve overall network performance) and expansion (adding more stations to the network). At the same time, we will discuss the role of various logistically and theoretically motivated measurement location placement restrictions and show how they influence the resulting network performance. Deployment of our statistical model and measurement network design selection algorithm will be illustrated on country-wide scale in the Czech Republic. The work has been done in cooperation with the Czech Hydrometeorological Institute and is related to the Technology Agency Czech Republic project ARAMIS, SS02030031).