It is needed to determine the change point of trend in the streamflow series.
MANN-KENDALL TEST: This is nonparametric test for monotnic trend. The test uses relative ranking of the data, not the trend itself. See attached file for reference and various types of trend analysis.
HYPOTHESIS: The null hypothesis is H0: no monotonic trend and the alternative is HA: monotonic trend exists. The Mann-Kendall test is given by verifying the Z-score of signs. The sum of signs is given by:
(1) S = Σ sign(Xk - Xi)
... where (Xk - Xi) represents all possible paired difference: [n(n - 1)] / 2. See link below for illustration. Once S is determined, use the Z-score equation to verify the level of significance according to our preset confidence interval for purposes of comparison and concluding. The Z score equation for S is given by:
(2) Za = (S - 1) / sqrt(var(S)) for S > 0
(3) Zb = 0 for S = 0
(4) Zc = (S + 1) / sqrt(var(S)) for S < 0
CHANGE POINT TREND: the change you are looking for is Za and Zb where Za > 1.65 or Zb > 1.65 for 95% confidence interval. See attached Z-Table.
REFERENCE: See attached articles and link.
http://vsp.pnnl.gov/help/Vsample/Design_Trend_Mann_Kendall.htm
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