Current Status of Time Series Analysis in Hydrological Sciences - Hydrologic Time Series Analysis: Theory and Practice - page 100

very well, two methods are reported to work slightly better than the others: the
standard normal homogeneity test without trend, and the multiple linear
regression technique.
Yue et al. (2003) proposed a trend-free pre-whitening (TFPW) procedure
to remove serial correlation from the time series, and hence to eliminate the
effect of serial correlation on the Mann-Kendall (MK) test. An additional
bootstrap test with the preservation of the cross correlation structure of a
network was proposed to assess the field significance of upward and downward
trends over the network separately. At the significance level of 5%, the site
significance of trends in the Canadian annual minimum, mean, and maximum
streamflows with 30-, 40- and 50-year records was assessed by the MK test
using the TFPW procedure (TFPW-MK). It was found that: (a) the 30-year
annual minimum and mean daily flows significantly decreased in the regions
of southern British Columbia (BC), around the centre of Prairie Provinces,
and in Atlantic Provinces, but they significantly increased in the region of
northern BC and Yukon Territory; and (b) the annual maximum flow
significantly decreased across southern Canada. The field significance of trends
over the whole country was evaluated by the bootstrap test at the significance
level of 5% and none of the three flow regimes experienced field-significant
changes.
Yue and Wang (2004) proposed effective sample size (ESS) to modify the
MK statistic for eliminating the effect of serial correlation on the MK test.
This study investigated the ability of ESS to eliminate the influence of serial
correlation on the MK test by Monte Carlo simulation. Simulation demonstrated
that when no trend exists within time series, ESS can effectively limit the
effect of serial correlation on the MK test. When trend exists within time
series, the existence of trend will contaminate the estimate of the magnitude
of sample serial correlation, and ESS computed from the contaminated serial
correlation cannot properly eliminate the effect of serial correlation on the
MK test. However, if ESS is computed from the sample serial correlation that
is estimated from the detrended series, ESS can still effectively reduce the
influence of serial correlation on the MK test.
Zhang et al. (2010a) developed a novel approach to identify trend patterns
of streamflows when trend is gradual or abrupt. The proposed approach uses
repeated monotonic trend tests with varying beginning and ending times. The
sensitivity of trends with respect to the period of time was then employed to
characterize the trend pattern. The proposed approach was demonstrated by
applying to watersheds within the Susquehanna River Basin, US. It was
observed that the new approach is capable of characterizing trend patterns. A
comparison with the results of single monotonic trend tests showed that the
novel approach is also useful for the exploration of all available data in
contrast to a single monotonic trend test that only shows trends for a specified
time period.