Geography Reference
In-Depth Information
The data mean shifted to a lower level around the year 1968 (marked as dashed
line) which reflects the documented drought of rainfall in this area (Dai et al.
2004
)Fig.
17.6
b shows an example of distribution change. The curves are the
distributions of global land temperature anomalies (with respect to the baseline
in 1951-1980) in different decades (Hansen et al.
2012
) which are approximately
normally distributed. As can be seen, the curves are shifting towards the right
where more high temperature are observed. This is considered as evidence of global
climate change (Hansen et al.
2012
). In spatial applications such as disease mapping,
the number of points (reports) in a spatial region is usually assumed to follow a
Poisson distribution. A change in the distribution indicates a higher risk of disease
(i.e., outbreak) in this area (Kulldorff
1997
).
As noted in Sect. 17.2, different applications may make different assumptions on
the underlying data distribution. Based on the assumption of the underlying data
distribution, statistical models can be classified as either parametric or the non-
parametric models. A parametric model may assumes the underlying distribution
is known. A non-parametric model may assume that the distribution is known
without the parameters being specified, or even that the distribution is not known.
For example, the top 5 % of the global temperature anomaly may be considered as
extremes. To identify a change in extreme level, a parametric model which assumes
that the data follows a normal distribution (e.g., like the curves shown in Fig.
17.6
b)
would simply compute, where and ยข are the mean and standard deviation of
the normal distribution. However, a non-parametric approach would compute the
5 % percentile of the dataset since the normality assumption does not hold in the
data.
Change patterns whose definitions are statistics-based include abrupt change
in time series (Basseville and Nikiforov
1993
), spatial clusters (e.g., outbreak of
disease or crimes) in spatial statistics (Kulldorff
1997
; Kulldorff and Nagarwalla
1995
), etc.
17.4
Change Pattern Families
In this section, we provide a taxonomy classifying different change patterns based
on their spatiotemporal footprints in the embedded ST framework. These ST
footprints includes points, intervals/curves, regions, and sub-spaces. A decision tree
classifying the output patterns and related techniques is given in Fig.
17.7
.These
change pattern can also be viewed from space and time perspectives respectively.
A temporal change pattern may include time points or intervals. A spatial change
pattern may include spatial location, paths and boundaries, and spatial regions. The
combinations of these two dimensions creates spatiotemporal output patterns, such
as spatiotemporal sub-spaces. Figure
17.8
shows a chart from this perspective.
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