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generalized extreme value (GEV) distribution (Khaliq et al., 2006
and references therein) and that of the nonparametric approach could be the
Mann-Kendall (MK) trend test (Mann, 1945; Kendall, 1975). Though
less widely used for the analysis of trends, the advantage of the parametric
approach is that it allows one to investigate trend as well as modelling of
hydrological observations. Compared to these aspects of the parametric
approach, the nonparametric approach allows investigation of trends
only. Based on the extensive literature survey, Machiwal and Jha (2008)
and Khaliq et al. (2009a) found that the nonparametric approach, particularly
the MK test, had been widely used for analyzing trends in hydrologic time
series. The reason for this inclination towards the nonparametric approach
could be fewer assumptions that are required for the application of this approach
compared to the parametric approach, wherein, among other factors, one
has to assume underlying distribution of data and type of the trend
model. Wide use of the MK test is just a coincidence because the equivalent
Spearman rank order correlation (SROC) test (Dahmen and Hall, 1990) is as
powerful as the MK test. To compare the ability of the SROC and MK tests
for identifying trends, Monte Carlo simulation method was used. Hundred
thousand samples were generated from the Normal and GEV (with shape
parameter equal to ±0.15) distributions, with mean and coefficient of variation
equal to unity, and each sample was superimposed by linear trends with
values ranging from -0.03 to 0.03, with an interval of 0.0025, before applying
the MK and SROC tests. Rejection rates of the null hypothesis of no trend
are shown in Fig. 10.1 that strongly support the above assertion, i.e. the power
of the MK and SROC tests in identifying trends, represented in terms of
rejection rates of the null hypothesis, is indistinguishable. It has been shown
in the literature (e.g., Yue et al., 2002a) that the trend identification ability of
the MK and SROC tests depends on the type of the underlying parent
distribution of the data. The results shown in Fig. 10.1 for samples of eight
different sizes generated from the Normal and GEV distributions also support
this observation.
It is important to mention here that least squares linear regression (Haan,
1977) that requires the data to be normally distributed is another parametric
approach that is also commonly used for the analysis of trends. Application of
the parametric approaches for investigation of trends in hydrological time
series is not addressed here. For that the reader is referred to Kundzewicz and
Robson (2000) and Khaliq et al. (2006), among others. Because of its popularity
and wide use, the MK trend test in its original and modified forms (to be
discussed later) is used for detailed analysis of trends in simulated and observed
data in the remainder of this chapter.
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