M. Bayazit

To prewhiten or not to prewhiten in trend analysis

Abstract The Mann-Kendall test, used to detect a trend in a time series, yields an incorrect (too large) rejection rate when applied to an autocorrelated series with no trend. Prewhitening corrects this situation, but reduces the power of the test when a trend exists. A simulation study is performed to determine when prewhitening can be applied with no real loss of power. It is found that, in general, prewhitening should be avoided when the test has a high power, i.e. when the coefficient of variation is very low, the slope of trend is high, and the sample size is large. In other cases, prewhitening will prevent the false detection of a non-existing trend, without a significant power loss in identifying a trend that exists.

Best-fit distributions of largest available flood samples

Abstract The longest available flood flow records are evaluated by various statistical procedures to determine the best fitting probability distributions. A total of 1819 site-years of data from 19 stations all over the world are analysed using seven methods. Although there are some differences in the results with respect to the site and the procedure, the generalized extreme value distribution is found to be superior to the other six distributions considered.

Effect of the occurrence process of the peaks over threshold on the flood estimates

Partial duration (peaks over threshold) series have been used as an alternative to annual maxima series in flood frequency analysis. Poisson process is usually assumed for the occurrence of peaks. In some peaks over threshold series, variance of the annual number of exceedances is significantly smaller (or larger) than the mean. In such cases binomial (or negative binomial) distribution has a better fit. Expressions are obtained for the estimation of the T-year flood and its sampling variance when binomial (or negative binomial) model is combined with the exponential distribution of peak magnitudes. It is shown that the results are almost identical to those obtained using the Poisson model, for which much simpler expressions are available.

A generalized seasonal model for flow duration curve

In this study a new method is developed to determine a flow duration curve (FDC) for a process in which stream flow is defined as a product of two variables, representing the periodic and the stochastic components, respectively. The cumulative frequency distribution is obtained via integration procedures and also given as an algorithm for discrete variables. Hence the exceedance probability for any given flow value can be calculated. The method is applied to daily flow data from many sites and it is found that the FDCs based on this method compare well with the observed FDC. Furthermore the FDCs developed in this method compare well with other methods in the recent literature. It was found that non-dimensional flow duration curves in Turkey can be characterized by three, or sometimes just two, parameters. Values of these parameters have been estimated at many sites enabling a FDC to be constructed at neighbouring sites for which only the drainage basin area is known. Copyright

Trends in the Maximum, Mean, and Low Flows of Turkish Rivers

Abstract 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...

Using wavelets for data generation

Wavelets are proposed as a non-parametric data generation tool. The idea behind the suggested method is decomposition of data into its details and later reconstruction by summation of the details randomly to generate new data. A Haar wavelet is used because of its simplicity. The method is applied to annual and monthly streamflow series taken from Turkey and USA. It is found to give good results for non-skewed data, as well as in the presence of auto-correlation.

Nonstationarity of Hydrological Records and Recent Trends in Trend Analysis: A State-of-the-art Review

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 as those resulting in over-preparedness. In a changing world, decision making in water resources management requires long-term projections of hydrological time series that include trend due to anthropogenic intervention and climate change.

Nonparametric streamflow simulation by wavelet or Fourier analysis

Abstract Wavelet or Fourier analysis is proposed as an alternative nonparametric method to simulate streamflows. An observed series is decomposed into its components at various resolutions and then recombined randomly to generate synthetic series. The mean and standard deviation are perfectly reproduced and coefficient of skewness tends to zero as the number of simulations increases. Normalizing transforms can be used for skewed series. Autocorrelation coefficients and the dependence structure are better preserved when Fourier analysis is used, but the mean and variance remain constant when the simulated and observed series have the same length. Monthly as well as annual flows can be simulated by this technique as illustrated on some examples. Wavelet analysis should be preferred as it generates flow series that exhibit a wider range of required reservoir capacities.

Probabilistic approach to modelling of recession curves

Abstract Recession curves of daily streamflow hydrographs are analysed by a probabilistic approach. Flow of a day on a recession curve is calculated by multiplying the previous days flow with a value of K smaller than one; K, defined as the ratio of the flows of successive days on the recession curve, was determined from observed daily flow time series. The range of K is divided into three class intervals. A procedure using the concept of gradually increasing values of K is adopted. For this, transition probabilities and average values of K are determined for each class interval and each month of the year. A recession curve can be generated, once the peak flow is known, by the probabilistic approach. The procedure allows nonlinear, seasonal and stochastic effects in flow recession of a river to be considered.

Markov Chain Models for Hydrological Drought Characteristics

AbstractEstimation of drought characteristics such as probabilities and return periods of droughts of various lengths is of major importance in drought forecast and management and in solving water resources problems related to water quality and navigation. This study aims at applying first- and second-order Markov chain models to dry and wet periods of annual streamflow series to reproduce the stochastic structure of hydrological droughts. Statistical evaluation of drought duration and intensity is usually carried out using runs analysis. First-order Markov chain model (MC1) for dry and wet periods is not adequate when autocorrelation of the original hydrological series is high. A second-order Markov chain model (MC2) is proposed to estimate the probabilities and return periods of droughts. Results of these models are compared with those of a simulation study assuming a lag-1 autoregressive [AR(1)] process widely used to model annual streamflows. Probability distribution and return periods of droughts of ...