  Fine particulate matter (PM2.5) measured at a given location is a mix of
pollution generated locally and pollution traveling long distances in the
atmosphere. Therefore, the identification of spatial scales associated with
health effects can inform on pollution sources responsible for these effects,
resulting in more targeted regulatory policy. Recently, prediction methods that
yield high-resolution spatial estimates of PM2.5 exposures allow one to
evaluate such scale-specific associations. We propose a two-dimensional wavelet
decomposition that alleviates restrictive assumptions required for standard
wavelet decompositions. Using this method we decompose daily surfaces of PM2.5
to identify which scales of pollution are most associated with adverse health
outcomes. A key feature of the approach is that it can remove the purely
temporal component of variability in PM2.5 levels and calculate effect
estimates derived solely from spatial contrasts. This eliminates the potential
for unmeasured confounding of the exposure - outcome associations by temporal
factors, such as season. We apply our method to a study of birth weights in
Massachusetts, U.S.A from 2003-2008 and find that both local and urban sources
of pollution are strongly negatively associated with birth weight. Results also
suggest that failure to eliminate temporal confounding in previous analyses
attenuated the overall effect estimate towards zero, with the effect estimate
growing in magnitude once this source of variability is removed.
