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are homogeneous. Based on the physical parameters affecting homogeneity,
the Cumulative Deviations test and the Bayesian test were found superior to
the classical von Neumann test. The performance of the Tukey test was found
excellent among all the multiple comparisons tests used in this study. The
results of the Bartlett test were found to be almost similar to that of the
Hartley test. The applicability of the Link-Wallace test, however, is limited
due to the basic assumption of equal sample size. Here, it is emphasized that
the history of data-recording stations should always be associated with the
time series records in order to assess the performance of different types of
homogeneity tests.
The rainfall time series of Kharagpur were found stationary at 5%
significance level based on the two parametric t -tests and one nonparametric
Mann-Whitney test. Out of the twelve trend-detecting tests applied, nine tests
revealed randomness (i.e., no trends) in all the seven rainfall time series.
Though the Wald-Wolfowitz Total Number of Runs test and the Spearman
Rank Order Correlation test reject the randomness in the annual rainfall time
series, this series is still considered random based on the results of other ten
tests (some of which such as Kendall's Rank Correlation and Mann-Kendall
tests are equally powerful in detecting randomness in the hydrologic time
series). Besides the results of three specific tests for stationarity, the results of
homogeneity and randomness tests also suggested stationarity in the annual
and maximum rainfall time series of Kharagpur. Furthermore, the Fourier
series analysis did not indicate apparent periodicity in any of the seven rainfall
series. The autocorrelation analysis indicated persistence in the annual rainfall
series with a time lag of nine years, though the deviation from the critical
value may not be considered significant for practical purpose. This observed
persistency in the annual rainfall series can be removed through transformations
(Machiwal and Jha, 2008).
Finally, it is concluded that the application of several statistical tests for
the same purpose in a time series analysis increases the chance for rejecting
a true null hypothesis. Therefore, the decision about the rejection of null
hypothesis should be made by critically analyzing the results of adequate
number of statistical tests (at least more than two tests). Such an approach for
time series analysis is essential to ensure efficient application of time series
tests in analyzing hydrologic time series, thereby enhancing the reliability of
time series tests in scientific decision making.
References
Abaurrea, J. and Cebrian, A. (2003). Trend analysis of daily rainfall extremes. http:/
/www.isi-eh.usc.es/resumenes/127_52_abstract.pdf (accessed on 27 July 2003).
Adamowski, K. and Bocci, C. (2001). Geostatistical regional trend detection in river
flow data. Hydrological Processes , 15: 3331-3341.
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