Trend analysis of annual sediment load
The Mann-Kendall (Kendall, 1975; Mann, 1945) test is a
non-parametric test to determine if trends can be identified in a
temporal series, including a seasonal component. This non-parametric
trends test is the result of an improved test initially studied by Mann
and updated by Kendall The test has 3 alternative hypotheses in the
series evolution: negative (i.e., decreasing trend), null (no trends in
the series), and positive (increasing trend) (Howden & Burt, 2009). The
Mann-Kendall Test statistic S is given as:
, where:
The variance of S denoted by is computed as:
where n is the number of data points, q is the number of tied
groups in the data set, and tj is the number of
data points in the jth tied group.
Then S and were used to compute the test statisticZs as:
A positive value of S indicates that there is an increasing trend
and a negative value indicates a decreasing trend. The null hypothesisH0 that there is no trend in the data is either
accepted or rejected depending if the computed ZSstatistics is less than or more than the critical value of Z-statistics
obtained from the normal distribution table at 5% significance level.
Pre-whitening (PW) is applied to remove the influence of
serial correlation on Mann-Kendall (Yue & Wang, 2002). The PWprocedure decreases the inflation of the variance of the test statistic
due to serials correlation, and thus reduces the rejection rate below
the rate before PW (Bayazit & Karpak, 2007).
Results