Bihrat Önöz

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.

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...

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.

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 ...

LL-moments for estimating low flow quantiles / Estimation des quantiles d'étiage grâce aux LL-moments

Abstract A parameter estimation method is proposed for fitting probability distribution functions to low flow observations. LL-moments are variants of L-moments that are analogous to LH-moments, which were defined for the analysis of floods. LL-moments give higher weights to the small observations. Expressions are given that relate them to the probability distribution function for the case of normal, Weibull and power distributions. Sampling properties of the LL-moments and of the distribution parameters and quantiles estimated by them are found by a Monte Carlo simulation study. It is shown on an example that the low flow quantile estimates obtained by LL-moments may be significantly different from those obtained by L-moments.

Troughs under threshold modeling of minimum flows in perennial streams

Troughs under threshold analysis has so far found little application in the modeling of minimum streamflows. In this study, all the troughs under a certain threshold level are considered in deriving the probability distribution of annual minima through the total probability theorem. For the occurrence of minima under the threshold, Poissonian, binomial or negative binomial processes are assumed. The magnitude of minima follows the generalized Pareto, exponential or power distribution. It is shown that asymptotic extreme value distributions for minima or the two-parameter Weibull distribution is obtained for the annual minima, depending on which models are assumed for the occurrence and magnitude of troughs under the threshold. Derived distributions can be used for modeling the minimum flows in streams which do not have zero flows. Expressions for the T-year annual minimum flow are obtained. An example illustrates the application of the troughs under threshold model to the minimum flows observed in a stream.

Integration of remote sensing and GIS for archaeological investigations

The western hinterland of the modern city of Istanbul contains some of the most remarkable monuments of ancient and medieval hydraulic engineering. Until recently fieldwork has been limited and only within the last two decades have there been serious attempts to map the complexity of the monuments and water lines. A GPS‐based archaeological survey has been undertaken by the authors and has been integrated with high resolution (IKONOS) and multi‐spectral spatial data giving the opportunity to view the system in its wider setting and also to identify major urban and landscape changes impacting on the long‐term conservation and management of the ancient remains.

REPLY to Discussion of “To prewhiten or not to prewhiten in trend analysis?”

We would like to thank the discusser for his interest in our paper. In the discussion it is argued that the simulation results should be expressed using the dimensionless parameter b/σx. The examples given in equations (1)–(4) show that the rejection rate of the null hypothesis of no trend depends on this parameter when the time series is uncorrelated. These examples have no relevance to the prewhitening process. The problem we have studied in our paper is rather different. We are not interested in simply finding the rejection rate of the no trend hypothesis, but our aim is to determine the power ratio PR, which we defined as the ratio of the power of the test for a correlated series after prewhitening (PW) to the power without PW for the same case when there is no serial dependence. This ratio is important because its value shows whether the prewhitening causes real loss of power. There is no reason to expect that PR will depend on b/σx. Our simulation results show clearly that it is not so. Consider for example two cases, in one of which Cv = 0.1 and b = 0.002, and in the other Cv = 0.5 and b = 0.01 (Cv corresponds to σx because the mean was equal to 1 in our simulations). In both cases b/σx = 0.02. For n = 25 and r = 0.2, Fig. 1 (Cv = 0.1, b = 0.002) gives PR = 1.3 whereas PR = 1.7 when Cv = 0.5, b = 0.01 (Fig. 3). Results are more drastically different for n = 25 and r = 0.8; PR = 0.8 (Fig. 1) compared with PR = 2.8 (Fig. 3). It can be concluded that PR depends not on b/σx, but on both b and σx. In our case study, we have made b dimensionless by dividing by the mean. But this does not invalidate our results as argued by the discusser, because we considered not only b but also Cv. Therefore, PR values obtained for the sites in the case study are correct. Dividing b by σx would lead to another set of figures instead of Figs 1–3, but the power ratios read from these figures for certain values of b/σx and σx (or Cv) would be the same as those obtained from our paper. We cannot agree within the final statement of the discussion that the question is not “To prewhiten or not to prewhiten?” but “How to prewhiten effectively?” As we have stated in the paper, it is very important to know when the prewhitening should be applied. If the prewhitening of a time series results in a real loss of power, it may cause an existing trend not to be detected. This is certainly not desired in trend studies, and therefore our results help answer the question in which cases prewhitening can be safely applied.