  Particulate matter (PM) is a class of malicious environmental pollutants
known to be detrimental to human health. Regulatory efforts aimed at curbing PM
levels in different countries often require high resolution space-time maps
that can identify red-flag regions exceeding statutory concentration limits.
Continuous spatio-temporal Gaussian Process (GP) models can deliver maps
depicting predicted PM levels and quantify predictive uncertainty. However, GP
based approaches are usually thwarted by computational challenges posed by
large datasets. We construct a novel class of scalable Dynamic Nearest Neighbor
Gaussian Process (DNNGP) models that can provide a sparse approximation to any
spatio-temporal GP (e.g., with non-separable covariance structures). The DNNGP
we develop here can be used as a sparsity-inducing prior for spatio-temporal
random effects in any Bayesian hierarchical model to deliver full posterior
inference. Storage and memory requirements for a DNNGP model are linear in the
size of the dataset thereby delivering massive scalability without sacrificing
inferential richness. Extensive numerical studies reveal that the DNNGP
provides substantially superior approximations to the underlying process than
low rank approximations. Finally, we use the DNNGP to analyze a massive air
quality dataset to substantially improve predictions of PM levels across Europe
in conjunction with the LOTOS-EUROS chemistry transport models (CTMs).
