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Abstract:Mann-Kendall (MK) test for trend detection must be modified when the data are serially correlated, to prevent the detection of false trends. Various approaches are developed for this purpose, such as prewhitening, trend-free prewhitening, variance correction and block bootstrap. Each method has its own Type I and Type II errors. In this study, the errors of block bootstrapping MK test are estimated by a simulation study and compared with other methods. Optimal block length that minimizes the Type I error is determined as function of sample size and autocorrelation coefficient. It is shown that the power of block bootstrapping MK test is comparable with those of other modified MK tests. These tests are applied to some annual streamflow series with trend recorded in Turkish rivers, and their powers are compared. A modified form of the trend-free prewhitening procedure is proposed that has a smaller Type I error.

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Recent climate change due to global warming has given an impetus to trend analysis of hydrological time series. Climate change as well as low-frequency climate variability and human intervention in river basins violate the assumption of stationarity, which is claimed to be dead by some researchers. Detailed climate models and long hydrological records are needed to predict the future conditions in a changing world. It must be remembered, however, that all hydrological systems include a stationary element, at least in the form of a random component. A stationary model is sometimes preferable to a nonstationary one when the evolution in time of hydrological processes cannot be predicted reliably. It is attempted to generate synthetic nonstationary time series of future climates by means of a global climate model, which are then used in water resources optimization under uncertainty. The estimation of extremes (floods and low flows) is more important but also much more difficult. The statistical significance of a trend can be detected by means of statistical tests such as the nonparametric Mann-Kendall test, which must be modified when there is serial correlation, possibly by prewhitening. Long-term persistence in hydrological processes also affects the results of the test. Some authors criticized the use of significance levels in statistical tests and recommended using confidence intervals around the estimated effect size. The power of a test depends on the chosen level of significance, sample size and the accuracy of prediction of trends. In some cases, it is more important to increase the power so that errors of estimation that may lead to damages due to inadequate protection are prevented. Frequency analysis of nonstationary processes can be made by fitting a trend to the parameters of the probability distribution. Annual maxima or peaks-over-threshold series can be analyzed incorporating a trend component to the parameters. Design concepts such as return period and hydrological risk should be redefined in a changing world. Design life level is another concept that can be used in a nonstationary context. In management decisions of water structures, a risk-based approach should be used where errors that result in under-preparedness are considered as well

In this study the existence of trend in maximum, mean, and low flows of Turkish rivers has been investigated. The data consisted of the daily mean flows of nearly 100 flow stations in 24 hydrological regions of Turkey. Trend analysis has been carried out using the parametric t test and nonparametric τ (Mann–Kendall) test. Both tests have been applied to annual maximum, mean, 1-day, and 7-day low flows. Trend existence was detected in the majority of rivers in western and southern Turkey and in some parts of central and eastern Turkey. Trends in mean and low flows were more common compared with maximum flows. Except at a few stations, flows showed a decreasing trend. In the time period of the last 30–60 yr, statistically significant decrease was found especially in the mean and low flows (and in some of the maximum flows) in western, central, and southern parts of Turkey. Such trends were not observed in other regions. These results are in agreement with those of the precipitation trend studies in Turkey.