Discussion of 'Trend, Independence, Stationarity, and Homogeneity Tests on Maximum Rainfall Series of Standard Durations Recorded in Turkey' by Tefaruk Haktanir and Hatice Citakoglu

摘要

In the original paper, Haktanir and Citakoglu employed the Mann-Kendall and linear regression trend test, von Neumann independence test, Wald-Wolfowitz stationarity test, and Mann-Whitney homogeneity test on the annual maximum rainfall (AMR) series of standard durations (namely, 5, 10, 15, 30 min and 1, 2, 3, 4, 5, 6, 8, 12, 18, and 24 h) in Turkey to (1) inspect the presence of monotonic trends and (2) evaluate the independency, stationarity, and homogeneity of AMR series of standard durations. However, the discussers would like to mention some additional points: 1. The Mann-Kendall test is a nonparametric test for trend detection of time series. The main advantage of this test is that the Mann-Kendall test does not specify whether the trend is linear or nonlinear. However, some researches show that existence of persistence, serial correlation, and scaling hypothesis can increase the probability of rejection of correct null hypothesis (Hamed 2008, 2009a, b). However, scaling behavior of AMR series is well known. It is possible to use a multifractal geometry to estimate intensity-duration-frequency (IDF) curves because of the existing scaling behavior of the AMR series. For example, Veneziano and Furcolo (2002) used scaling behavior of a 24-h AMR serie to estimate IDF curves. Therefore, it was more convenient that the authors considered scaling behavior of AMR series with the Mann-Kendall trend test. Moreover, time series persistence can be defined by the Hurst coefficient (H). For a Brownian motion process, H tends to be 0.5, but persistent series increases by increasing H. The calculation procedure of H can be found in Hurst (1951) and McLeod and Hipel (1978). To show the existence of persistence in the AMR series, some AMR series were recorded at Merzifon, Turkey, which are tabulated in Table 2 of the original paper. The corresponding H is calculated and presented in Table 1. Considering Table 1, the H of some AMR series is bigger than 0.5. Thus, they can be categorized as persistent time series. It can also be seen from Table 1 that with increasing AMR duration, H increases. So it can be concluded that at the Merzifon, Turkey, station, by increasing the AMR duration, the rejection probability of the null correct hypothesis of the Mann-Kendall test increases. Therefore, if the same relation between AMR durations and H can be found in other studied stations, the results in Table 6 of the original paper should be clarified. Table 6 shows that more trends are detected in the longer durations. Regarding Table 1 and based on Hamed's (2009b) results, it can be concluded that some of the detected trends in Table 6 for longer durations of AMR series (e.g., 18 and 24 h) are caused by incapability of the Mann-Kendall test for detecting trend of persistent time series. Therefore, it could be more convenient that the authors considered the Mann-Kendall test for persistent time series instead of applying the classical Mann-Kendall test because the applied data show the persistent behavior.