Extreme events over time - Extreme Events: A Physical Reconstruction and Risk Assessment - page 259

0.080

0.060

0.040

0.020

0.000

− 4000 − 2000 0 2000

Calendar year

Figure 10.1. Cumulative probability frequency of 14 C (uncorrected) ages for the
northwest coast of Western Australia (from Nott and Bryant, 2003 ).

of an event, as mentioned in Chapter 1,suggests that events in a time series
occur independently of each other and, therefore, are not cyclic. Figures 10.2
and 10.3 show the results of two separate statistical analyses for serial correla-
tion of several of the long-term high-resolution records of the natural hazards
discussed in earlier chapters. Each of the records is an annual register of cen-
tury to millennial length. Some natural hazards, such as tropical cyclones, do
not occur annually and cannot, therefore, be analysed in this manner. However,
some of the forcing mechanisms responsible for the frequency of occurrence
of these hazards (Nichols, 1984)dooccur annually and can be included in the
statistical analysis. These records include sea-surface temperatures (SST), North
Atlantic Oscillation (NAO), Pacific Decadal Oscillation (PDO), El Nino Southern
Oscillation (ENSO) and rainfall.
Figure 10.2 displays the results of a Runs test on a variety of natural hazards
such as North American droughts as recorded by tree rings, stream discharges,
rainfall years from speleothem layers in China, Scotland and Australia, coral
layer density, along with SST, NAO, PDO and ENSO. The Runs test examines the
number and length of increasing and decreasing runs or trends in a time series.
Forexample a time series may be composed of a sequence where the trend is
increasing (e.g. 1, 2, 3, 4, 5) and then a shorter run of decreasing numbers (e.g.
7, 6, 5). The number and length of these individual runs is compared to that
expected from a series of random events. The null hypothesis is that the time
series is random and the test statistic is represented by the Z score. Where the Z
score exceeds approximately 1.9, the null hypothesis can be rejected at the 0.05
significance level. Three separate tests were also undertaken on a series of ran-
domly generated numbers to highlight the pattern expected if the time series of
natural hazards and events were truly random. Each of the time series was also
analysed at cumulative incremental time lengths with 50--100 year intervals. In
other words, the Runs test was undertaken on the first 50 or 100 years of record,