Geoscience Reference
In-Depth Information
1
4
1 Sanctuary Is. annual coral band density
2
7
2. Agincourt reef annual coral band density
3
5
0.8
3 Pacific Decadal Oscillation
4 White River discharge
6
0.6
11
5 Roratonga sea surface temperatures
8
6 Palmer Drought Severity Index (USA)
0.4
10
0.05 probability
limits
7 Southern Oscillation Index
8 New Mexico tree rings (precipitation)
9
0.2
9 Burdekin River discharge
10 Chillagoe speleothem layer thickness
0.0
0.0
11 North Atlantic Oscillation
0.1
0.2
0.3
0.4
Figure 10.4.
Results from cumulative periodograms for serial correlation. (Data
from 1, 2, Lough and Barnes,
2000
; Chalker and Barnes,
1990
;3,Biondi
et al
.,
2001
;
4, Cleaveland,
2000
;5,Linsley
et al
.,
2000
;6,Cook,
2000
;7,Allen
et al
.,
1996
;Stahle
et al
.,
1998
;8,Grissino-Mayer,
1996
;9,Isedale
et al
.,
1998
;11, Cook,
et al
.,
2002
.)
series. A lag is a comparison or relationship between events of a certain distance
apart in the sequence. For example a lag of two compares events separated by
one event (or every second event), a lag of three compares events separated by
two events and a lag of four or five are comparisons between events three and
four events apart respectively, throughout the length of the time series. The
time series examined using the Ljung-box test were also analysed over various
length--time intervals and as seen in Figure 10.3 all of the curves except for the
random numbers also show steep upward trends and exceed the 0.05 probability
level. Like the Runs test, the Ljung-box test has a null hypothesis that the time
series is random. When the test statistic exceeds the 0.05 probability level there
is a 95% chance that the time series is not random and therefore is serially
correlated or shows auto correlation at certain lags. Again the null hypothe-
sis of randomness in the time series examined can be rejected after 100--200
years ofrecord; indeed in some cases it can be rejected after just 50 years
of record. The time series were also examined using cumulative periodograms
(Fig. 10.4), which test for the probability that the events in a time series repre-
sent 'white noise' or randomness. The time series can be regarded as non-random
when the line extends outside of the 95% confidence limits. As with the Runs
and Ljung-box tests, the cumulative periodograms highlight that time series of
both natural hazards and natural events such as SST, PDO, NAO, ENSO and rain-
fall regularly display serial correlation over time. The first part of the record
(
∼
100years), however, commonly appears as white noise suggesting that this
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