There is continuing interest in the investigation of change in temperature
over space and time. We offer a set of tools to illuminate such change
temporally, at desired temporal resolution, and spatially, according to region
of interest, using data generated from suitable space-time models. These tools
include predictive spatial probability surfaces and spatial extents for an
event. Working with exceedance events around the center of the temperature
distribution, the probability surfaces capture the spatial variation in the
risk of an exceedance event, while the spatial extents capture the expected
proportion of incidence of a given exceedance event for a region of interest.
Importantly, the proposed tools can be used with the output from any suitable
model fitted to any set of spatially referenced time series data.
As an illustration, we employ a dataset from 1956 to 2015 collected at 18
stations over Arag\'{o}n in Spain, and a collection of daily maximum
temperature series obtained from posterior predictive simulation of a Bayesian
hierarchical daily temperature model. The results for the summer period show
that although there is an increasing risk in all the events used to quantify
the effects of climate change, it is not spatially homogeneous, with the
largest increase arising in the center of Ebro valley and Eastern Pyrenees
area. The risk of an increase of the average temperature between 1966-1975 and
2006-2015 higher than 1∘C is higher than 0.5 all over the region, and
close to 1 in the previous areas. The extent of daily temperature higher than
the reference mean has increased 3.5% per decade. The mean of the extent
indicates that 95% of the area under study has suffered a positive increment of
the average temperature, and almost 70% higher than 1∘C.Comment: 23 pages main manuscript and 7 pages supplemen