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2-day maximum rainfall series, three phases of lengths 1, 2 and 3 were
encountered, whereas in case of annual and 3-, 4-, 5- and 6-day maximum
rainfall time series, phases with lengths of 1, 2, 3 and 4 were found. The
observed and expected numbers of phase lengths are given in Table 7.5. It is
apparent from Table 7.5 that the differences between the observed and expected
numbers of individual phases are small for the annual rainfall time series,
whereas the differences are significant for the maximum rainfall series of all
durations. Thus, the Kendall's Phase test indicates absence of trend in the
annual rainfall time series and presence of trend in all the maximum rainfall
time series of Kharagpur.
The results of the linear model or Regression test are summarized in
Table 7.6. It is clear from this table that the computed values of the test-
statistic are less than their critical values (±1.96) for all the rainfall time series
under study, which suggests that the annual and maximum rainfalls of
Kharagpur do not have any linear trends. However, the computed test-statistic
value (1.78) for the nonparametric Spearman Rank Order Correlation (SROC)
test is greater than its critical value (1.681) for the annual rainfall time series
(Table 7.6), and hence the null hypothesis of no trend is rejected. Thus, the
annual rainfall series of Kharagpur has a trend based on the SROC test. On the
other hand, results of the SROC test indicate that one-day, 2-, 3-, 4-, 5- and 6-
day maximum rainfalls of Kharagpur are trend-free. Similarly, the annual and
maximum rainfall series were found not to have any trend based on the
Turning Point test (Table 7.6). On the contrary, the results of the Wald-
Wolfowitz Total Number of Runs test indicated trends for all the seven rainfall
time series. Furthermore, it can also be seen from Table 7.6 that the computed
values of the Sum of Squared Lengths test-statistic vary from 49 to 67 for all
the seven rainfall time series, which are considerably less than its critical
value (>118). This suggests no trend in any of the rainfall series. The computed
and critical values of the test-statistic of the Adjacency and the Difference
Sign tests are also compared in Table 7.6, which reveals that all the rainfall
series are free from any kind of trend. However, based on the Difference Sign
test, the 4-day maximum rainfall series has some trend, but the remaining six
rainfall series are trend-free.
Finally, a comparison between the computed and critical values of the
test-statistics of Run test on Successive Differences (Table 7.6) reveals that
the annual rainfall series and all the maximum rainfall time series of Kharagpur
are trend-free at 5% significance level. Thus, the results of the four tests (i.e.,
Run test on Successive Differences, Inversions test, Kendall's Rank Correlation
test and Mann-Kendall test) are similar to each other (Table 7.6). It can also
be seen that the computed test-statistic values of the Kendall's Rank Correlation
test are closely related to that of the Mann-Kendall test, which emphasizes the
equal power of both the tests in detecting a trend in hydrologic time series.
This might be the reason that of these four tests, the Kendall's Rank Correlation
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