  This paper outlines a methodology for semi-parametric spatio-temporal
modelling of data which is dense in time but sparse in space, obtained from a
split panel design, the most feasible approach to covering space and time with
limited equipment. The data are hourly averaged particle number concentration
(PNC) and were collected, as part of the Ultrafine Particles from Transport
Emissions and Child Health (UPTECH) project. Two weeks of continuous
measurements were taken at each of a number of government primary schools in
the Brisbane Metropolitan Area. The monitoring equipment was taken to each
school sequentially. The school data are augmented by data from long term
monitoring stations at three locations in Brisbane, Australia.
  Fitting the model helps describe the spatial and temporal variability at a
subset of the UPTECH schools and the long-term monitoring sites. The temporal
variation is modelled hierarchically with penalised random walk terms, one
common to all sites and a term accounting for the remaining temporal trend at
each site. Parameter estimates and their uncertainty are computed in a
computationally efficient approximate Bayesian inference environment, R-INLA.
  The temporal part of the model explains daily and weekly cycles in PNC at the
schools, which can be used to estimate the exposure of school children to
ultrafine particles (UFPs) emitted by vehicles. At each school and long-term
monitoring site, peaks in PNC can be attributed to the morning and afternoon
rush hour traffic and new particle formation events. The spatial component of
the model describes the school to school variation in mean PNC at each school
and within each school ground. It is shown how the spatial model can be
expanded to identify spatial patterns at the city scale with the inclusion of
more spatial locations.
