  The last two decades have seen intense scientific and regulatory interest in
the health effects of particulate matter (PM). Influential epidemiological
studies that characterize chronic exposure of individuals rely on monitoring
data that are sparse in space and time, so they often assign the same exposure
to participants in large geographic areas and across time. We estimate monthly
PM during 1988--2002 in a large spatial domain for use in studying health
effects in the Nurses' Health Study. We develop a conceptually simple
spatio-temporal model that uses a rich set of covariates. The model is used to
estimate concentrations of $PM_{10}$ for the full time period and $PM_{2.5}$
for a subset of the period. For the earlier part of the period, 1988--1998, few
$PM_{2.5}$ monitors were operating, so we develop a simple extension to the
model that represents $PM_{2.5}$ conditionally on $PM_{10}$ model predictions.
In the epidemiological analysis, model predictions of $PM_{10}$ are more
strongly associated with health effects than when using simpler approaches to
estimate exposure. Our modeling approach supports the application in estimating
both fine-scale and large-scale spatial heterogeneity and capturing space--time
interaction through the use of monthly-varying spatial surfaces. At the same
time, the model is computationally feasible, implementable with standard
software, and readily understandable to the scientific audience. Despite
simplifying assumptions, the model has good predictive performance and
uncertainty characterization.
