  Environmental problems are receiving increasing attention in socio-economic
and health studies. This in turn fosters advances in recording and data
collection of many related real-life processes. Available tools for data
processing are often found too restrictive as they do not account for the rich
nature of such data sets. In this paper, we propose a new statistical
perspective on forecasting spatial environmental data collected sequentially
over time. We treat this data set as a surface (functional) time series with a
possibly complicated geographical domain. By employing novel techniques from
functional data analysis we develop a new forecasting methodology. Our approach
consists of two steps. In the first step, time series of surfaces are
reconstructed from measurements sampled over some spatial domain using a finite
element spline smoother. In the second step, we adapt the dynamic functional
factor model to forecast a surface time series. The advantage of this approach
is that we can account for and explore simultaneously spatial as well as
temporal dependencies in the data. A forecasting study of ground-level ozone
concentration over the geographical domain of Germany demonstrates the
practical value of this new perspective, where we compare our approach with
standard functional benchmark models.
