  Mexico City tracks ground-level ozone levels to assess compliance with
national ambient air quality standards and to prevent environmental health
emergencies. Ozone levels show distinct daily patterns, within the city, and
over the course of the year. To model these data, we use covariance models over
space, circular time, and linear time. We review existing models and develop
new classes of nonseparable covariance models of this type, models appropriate
for quasi-periodic data collected at many locations. With these covariance
models, we use nearest-neighbor Gaussian processes to predict hourly ozone
levels at unobserved locations in April and May, the peak ozone season, to
infer compliance to Mexican air quality standards and to estimate respiratory
health risk associated with ozone. Predicted compliance with air quality
standards and estimated respiratory health risk vary greatly over space and
time. In some regions, we predict exceedance of national standards for more
than a third of the hours in April and May. On many days, we predict that
nearly all of Mexico City exceeds nationally legislated ozone thresholds at
least once. In peak regions, we estimate respiratory risk for ozone to be 55%
higher on average than the annual average risk and as much at 170% higher on
some days.
